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4
3
2
1
Outside the middle school program
/ Arithmetic
31 exercises (100% corrected)
a
First notions of PGCD
(3 exercices)
Euclid's Algorithm: GCD
(8 exercices)
Euclid's Algorithm: Coprime Numbers
(3 exercices)
Euclid's Algorithm: GCD and Modeling
(14 exercices)
PPCM
(2 exercices)
Us-math : GCF
(1 exercice)
Dividende
Diviseur
Reste
6452
3241
...
...
...
...
...
...
...
...
...
...
×
6452
...
3241
...
×
...
...
...
...
×
...
...
...
...
×
...
...
...
...
Dividende
Diviseur
Reste
645
596
...
...
...
...
...
...
...
...
...
...
×
645
...
596
...
×
...
...
...
...
×
...
...
...
...
×
...
...
...
...
1.
First
notions
of
PGCD
E.630
A
carp
en
ter
mak
es
iden
tical
planks
of
w
o
o
d,
eac
h
with
a
thic
kness
of
a
whole
n
um
b
er
of
cen
timeters.
A
t
the
end
of
his
w
ork,
he
has
t
w
o
piles
of
planks
:
The
first
pile
has
a
total
heigh
t
of
30
cm
;
the
second
heap
has
a
total
heigh
t
of
42
cm
.
1
a
Giv
e
the
list
of
eigh
t
divisors
of
30
and
the
list
of
eigh
t
divisors
of
42
.
b
What
are
the
p
ossible
measuremen
ts
of
the
thic
kness
c
hosen
b
y
the
joiner?
2
In
eac
h
case,
giv
e
the
n
um
b
er
of
b
oards
a
v
ailable
to
the
joiner.
E.629
A
florist
has
126
irises
and
210
roses.
He
w
an
ts,
using
all
his
flo
w
ers,
to
mak
e
iden
tical
b
ouquets
eac
h
con
taining
irises
and
roses.
Justify
all
answ
ers
to
the
questions
b
elo
w
:
1
Justify
that
it
can
mak
e
14
b
ouquets.
What
is
the
com-
p
osition
of
a
b
ouquet?
2
Under
these
constrain
ts,
justify
that
he
cannot
mak
e
15
b
ouquets.
E.615
1
Giv
e
the
sev
en
divisors
of
64
and
the
eigh
t
24
.
2
Giv
e
the
irreducible
form
of
the
fraction
24
64
.
3
Marc
o
wns
64
red
candies
and
24
blue
candies.
He
w
an
ts
to
create
candy
pac
k
ages
where
:
eac
h
pac
k
age
con
tains
the
same
n
um
b
er
of
red
candies
and
the
same
n
um
b
er
of
blue
candies
;
all
candies
m
ust
b
e
used.
The
follo
wing
notations
are
used
:
k
:
n
um
b
er
of
pac
k
ets
made
x
:
n
um
b
er
of
red
candies
for
eac
h
pac
k
y
:
n
um
b
er
of
blue
candies
for
eac
h
paquet
a
Find
a
relationship
b
et
w
een
the
n
um
b
ers
k
,
x
,
y
,
64
and
24
.
b
Deduce
the
maxim
um
n
um
b
er
of
pac
k
ages
Marc
can
mak
e
and
the
n
um
b
er
of
blue
and
red
candies
con-
tained
in
eac
h.
2.
Euclid’s
A
lgorithm
:
GCD
E.602
1
T
o
calculate
the
PGCD
of
the
in
tegers
6452
and
3241
,
complete
the
follo
wing
table
using
Euclid’s
algorithm
:
2
What
can
w
e
sa
y
ab
out
the
in
tegers
6452
and
3241
?
E.642
1
Using
Euclid’s
algorithm,
complete
the
table
b
elo
w
to
determine
the
P
GC
D
of
the
in
tegers
645
and
596
:
2
What
can
w
e
sa
y
ab
out
the
in
tegers
645
and
596
?
E.640
Consider
the
fraction
E
=
108
288
.
1
Wh
y
is
the
fraction
E
not
irreducible?
(Justify
with
no
c
alculations)
2
Calculate
the
P
GC
D
of
108
and
288
.
3
W
rite
the
fraction
E
in
irreducible
form.
E.625
1
Are
the
in
tegers
1018
and
324
prime
with
eac
h
other?
Justify
y
our
answ
er.
2
Calculate
the
greatest
common
divisor
of
1018
and
324
.
3
Simplify
the
fraction
324
1018
to
mak
e
it
irreducible.
E.628
1
Calculate
the
Greatest
Common
Divisor
(PGCD)
of
496
and
806.
2
W
rite
496
806
as
an
irreducible
fraction.
3
Calculate
:
496
806
−
3
26
(we
wil
l
give
the
r
esult
as
an
irr
e
ducible
fr
action)
E.626
Use
an
y
metho
d
y
ou
lik
e
to
mak
e
the
follo
wing
fractions
irreducible
:
a
24
68
c
416
224
b
16
302
8398
E.610
Use
the
metho
d
of
y
our
c
hoice
to
mak
e
the
follo
wing
fractions
irreducible.
a
35
45
b
168
312
c
6546
2584
h
ttps:/
/c
hingmath.fr
chapExoCorrec/630
sacados/630
faire en sorte qu il n y a qu une epaisseur de planche possible
chapExoCorrec/629
sacados/629
chapExoCorrec/615
sacados/615
chapExoCorrec/602
sacados/602
Dividende
Diviseur
Reste
6452
3241
...
...
...
...
...
...
...
...
...
...
×
6452
...
3241
...
×
...
...
...
...
×
...
...
...
...
×
...
...
...
...
chapExoCorrec/642
sacados/642
Dividende
Diviseur
Reste
645
596
...
...
...
...
...
...
...
...
...
...
×
645
...
596
...
×
...
...
...
...
×
...
...
...
...
×
...
...
...
...
chapExoCorrec/640
sacados/640
chapExoCorrec/625
sacados/625
chapExoCorrec/628
sacados/628
Groupe Est - Septembre 2002 - 3 points
chapExoCorrec/626
sacados/626
chapExoCorrec/610
sacados/610
1
2
3
4
5
6
A
B
C
216
126
90
54
36
18
126
90
36
36
18
18
90
36
54
18
18
0
Dividende
Diviseur
Reste
240
36
...
...
...
...
...
...
...
×
240
...
36
...
×
...
...
...
...
×
...
...
...
...
E.6297
Here’s
a
spreadsheet
obtained
using
a
spreadsheet
program.
In
this
exercise,
w
e
try
to
understand
ho
w
this
sheet
w
as
filled
in.
1
Lo
oking
at
the
v
alues
in
the
table,
sug-
gest
a
form
ula
to
en
ter
in
cell
C1
,
then
cop
y
do
wn.
2
In
this
question,
all
traces
of
re-
searc
h
will
b
e
left
on
the
cop
y
.
They
will
b
e
v
alued.
The
spreadsheet
pro
vides
t
w
o
functions
MAX
and
MIN
.
F
rom
t
w
o
n
um
b
ers,
MAX
returns
the
larger
v
alue
and
MIN
the
smaller.
(example
MAX(23
;12)=23
)
.
Whic
h
form
ula
w
as
en
tered
in
cell
A2
,
then
copied
do
wn?
2
What
do
es
the
n
um
b
er
in
cell
C5
represen
t,
in
relation
to
the
n
um
b
ers
216
and
126
?
3
Is
the
fraction
216
126
irreducible?
If
not,
mak
e
it
irreducible
b
y
detailing
the
calculations.
3.
Euclid’s
A
lgorithm
:
Coprime
Numb
ers
E.616
1
Calculate
the
PGCD
of
the
in
tegers
1183
and
455
,
sp
ec-
ifying
the
metho
d
used.
2
W
rite
in
irreducible
form
the
fraction
1183
455
(Details
of
c
alculations
should
b
e
given)
E.646
1
Are
the
in
tegers
2464
and
924
prime
with
eac
h
other?
Justify
.
2
Calculate
the
P
GC
D
of
2464
and
924
.
3
Giv
e
the
sum
2464
924
+
5
6
as
an
irreducible
fraction
E.5181
Here
are
the
answ
ers
prop
osed
b
y
a
studen
t
to
an
exercise.
F
or
eac
h
answ
er,
explain
wh
y
it
is
correct
or
incorrect.
1
x
2
−
81
=
(
x
−
9)
2
2
(
x
−
3)(
x
+
5)
=
(
x
+
1)
2
−
16
3
The
in
tegers
735
and
674
are
prime
to
eac
h
other.
4.
Euclid’s
A
lgorithm
:
GCD
and
Mo
deling
E.643
A
florist
has
240
tulips
and
36
orc
hids.
He
w
an
ts
to
use
all
the
flo
w
ers
in
his
p
ossession
to
mak
e
as
man
y
b
ouquets
as
p
ossible,
eac
h
con
taining
the
same
n
um
b
er
of
tulips
and
the
same
n
um
b
er
of
orc
hids.
1
W
e
note
:
k
:
the
n
um
b
er
of
b
ouquets
made.
x
:
the
n
um
b
er
of
tulips
making
up
eac
h
b
ouquet.
y
:
the
n
um
b
er
of
orc
hids
making
up
eac
h
b
ouquet.
W
rite
the
in
tegers
240
and
36
using
k
,
x
and
y
.
2
What
do
es
the
in
teger
k
represen
t
for
the
t
w
o
in
tegers
240
and
36
.
Sp
ecify
.
3
Apply
Euclid’s
algorithm
to
the
follo
wing
in
tegers
240
and
36
:
4
Sp
ecify
the
n
um
b
er
of
b
ouquets
the
florist
will
b
e
able
to
mak
e
and
the
n
um
b
er
of
orc
hids
and
tulips
included
in
eac
h.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6297
sacados/6297
1
2
3
4
5
6
A
B
C
216
126
90
54
36
18
126
90
36
36
18
18
90
36
54
18
18
0
chapExoCorrec/616
sacados/616
Groupe Nord - Juin 2003 - 2 points
chapExoCorrec/646
sacados/646
chapExoCorrec/5181
sacados/5181
chapExoCorrec/643
sacados/643
Dividende
Diviseur
Reste
240
36
...
...
...
...
...
...
...
×
240
...
36
...
×
...
...
...
...
×
...
...
...
...
Dividende
Diviseur
Reste
248
32
...
...
...
...
...
...
...
×
248
...
32
...
×
...
...
...
...
×
...
...
...
...
E.603
A
shopk
eep
er
has
248
stra
wb
erry
candies
and
32
min
t
can-
dies.
He
w
an
ts
to
mak
e
as
man
y
pac
k
ages
of
stra
wb
erry
candies
and
min
t
candies
as
p
ossible.
He
w
an
ts
to
use
all
the
candies
he
has,
and
eac
h
pac
k
age
m
ust
con
tain
the
same
n
um
b
er
of
candies.
T
o
solv
e
this
problem,
complete
the
follo
wing
exercise
:
Let’s
use
the
follo
wing
notation
:
k
:
le
nom
bre
de
b
on
b
ons
dans
c
haque
paquet
x
:
le
nom
bre
de
paquets
à
la
fraise
y
:
le
nom
bre
de
paquets
à
la
men
the
W
e
ha
v
e
the
follo
wing
relationships
in
terms
of
k
,
x
,
and
y
:
248
=
:
:
:
:
:
:
×
:
:
:
:
:
:
;
32
=
:
:
:
:
:
:
×
:
:
:
:
:
:
The
in
teger
:
:
:
:
:
:
is
therefore
a
divisor
of
the
in
tegers
248
and
32
:
since
he
w
an
ts
to
mak
e
as
man
y
pac
k
ages
as
p
ossible,
this
n
um
b
er
is
.
.
.
.
.
.
of
248
and
32
.
A
ccording
to
Euclid’s
algorithm,
w
e
ha
v
e
:
F
rom
this,
w
e
deduce
:
P
GC
D
(
248
;
32
)
=
:
:
:
:
:
:
W
e
ha
v
e
the
follo
wing
t
w
o
calculations
:
248
:
:
:
:
:
:
=
:
:
:
:
:
:
;
32
:
:
:
:
:
:
=
:
:
:
:
:
:
Th
us,
the
shopk
eep
er
will
prepare
:
:
:
:
:
:
stra
wb
erry-fla
v
ored
pac
k
ages
and
:
:
:
:
:
:
min
t-fla
v
ored
pac
k
ages,
eac
h
con
taining
:
:
:
:
:
:
pieces
of
candy
.
E.3550
1
Are
the
in
tegers
198
and
144
prime
with
eac
h
other?
Jus-
tify
the
answ
er
without
doing
an
y
calculation
.
2
Calculate
the
P
GC
D
of
198
and
144
detailing
the
metho
d.
3
W
rite
the
fraction
144
198
in
irreducible
form.
Explain
the
metho
d.
4
On
the
mark
et,
a
pro
ducer
has
198
zucc
hinis
and
144
eggplan
ts.
With
all
the
v
egetables,
he
mak
es
tra
ys
all
comp
osed
iden
tically
.
He
uses
as
man
y
tra
ys
as
p
ossible.
a
Ho
w
man
y
tra
ys
do
es
he
use?
b
Ho
w
man
y
zucc
hinis
and
eggplan
ts
do
es
eac
h
tra
y
con-
tain?
E.3545
1
Determine
the
P
GC
D
of
1
394
and
255
.
2
A
craftsman
has
1
394
acai
seeds
and
255
p
eac
h
palm
seeds.
He
w
an
ts
to
mak
e
iden
tical
nec
klaces,
i.e.
eac
h
con
tain-
ing
the
same
n
um
b
er
of
acai
seeds
and
the
same
n
um
b
er
of
p
eac
h
palm
seeds.
a
Ho
w
man
y
nec
klaces
at
most
can
he
mak
e
using
all
his
seeds?
b
In
this
case,
ho
w
man
y
acai
seeds
and
p
eac
h
palm
seeds
do
es
eac
h
nec
klace
con
tain?
E.2353
1
Calculate
the
P
GC
D
of
110
and
88
.
2
a
A
w
ork
er
has
metal
plates
110
cm
long
and
88
cm
wide.
He
w
as
giv
en
the
follo
wing
instructions
:
ˇDécoup
er
in
these
plates
squares
all
iden
tical,
as
large
as
p
ossible,
so
as
to
ha
v
e
no
loss.ı
What
will
b
e
the
length
of
the
side
of
a
square?
b
Ho
w
man
y
squares
will
he
get
p
er
plate?
E.611
1
Determine
the
PGCD
of
the
in
tegers
108
and
135
.
2
Marc
has
108
red
marbles
and
135
blac
k
marbles.
He
w
an
ts
to
mak
e
pac
k
ets
so
that
:
all
pac
k
ets
con
tain
the
same
n
um
b
er
of
blac
k
marbles
;
all
pac
ks
con
tain
the
same
n
um
b
er
of
red
marbles
;
all
red
marbles
and
all
blac
k
marbles
are
used.
a
What
maxim
um
n
um
b
er
of
pac
k
ets
will
it
b
e
able
to
ac
hiev
e?
b
Ho
w
man
y
red
and
blac
k
marbles
will
there
then
b
e
in
eac
h
pac
k?
E.614
1
a
Calculate
the
P
GC
D
of
494
and
43.
b
What
can
y
ou
sa
y
ab
out
these
t
w
o
in
tegers?
c
Is
the
fraction
494
43
reducible?
2
a
Calculate
the
P
GC
D
of
396
and
252.
A
jew
eler
o
wns
396
rubies
and
252
diamonds.
He
wishes
to
comp
ose
as
man
y
rings
as
p
ossible
suc
h
that
eac
h
has
the
same
n
um
b
er
of
rubies
and
the
same
n
um
b
er
of
diamonds.
b
Ho
w
man
y
rings
can
he
mak
e?
h
ttps:/
/c
hingmath.fr
chapExoCorrec/603
sacados/603
Dividende
Diviseur
Reste
248
32
...
...
...
...
...
...
...
×
248
...
32
...
×
...
...
...
...
×
...
...
...
...
chapExoCorrec/3550
sacados/3550
chapExoCorrec/3545
sacados/3545
chapExoCorrec/2353
sacados/2353
chapExoCorrec/611
sacados/611
Groupe Ouest - 2001 - ? points
chapExoCorrec/614
sacados/614
E.3459
A
salesman
has
a
sto
c
k
of
276
p
ostcards
and
230
k
ey
rings.
He
w
an
ts
to
mak
e
ˇ
Souv
enirs
de
T
ahiti
and
his
Îles
ı
b
o
xes
so
that
:
the
n
um
b
er
of
p
ostcards
in
eac
h
b
o
x
is
the
same
;
the
n
um
b
er
of
k
ey
rings
b
e
the
same
in
eac
h
b
o
x
;
all
p
ostcards
and
k
ey
rings
b
e
used.
1
Ho
w
man
y
b
o
xes,
eac
h
con
taining
10
k
ey
rings,
will
he
b
e
able
to
mak
e?
Ho
w
man
y
p
ostcards
will
eac
h
b
o
x
then
con
tain?
2
a
Calculate
the
P
GC
D
of
276
and
230
,
detailing
the
metho
d
used.
b
What
is
the
maxim
um
n
um
b
er
of
b
o
xes
the
seller
can
mak
e?
Ho
w
man
y
k
ey
rings
and
p
ostcards
will
eac
h
b
o
x
con-
tain?
E.619
1
Sho
w
that
the
PGCD
of
the
in
tegers
372
and
775
is
equal
to
31
;
write
the
calculations.
2
A
conductor
has
372
male
and
775
female
c
horisters
rehearsing
for
a
concert.
He
w
an
ts
to
mak
e
rehearsal
groups
so
that
:
The
n
um
b
er
of
female
c
horisters
in
eac
h
group
is
the
same
;
The
n
um
b
er
of
male
c
horisters
is
the
same
in
eac
h
group
;
eac
h
c
horister
b
elongs
to
one
group.
a
What
maxim
um
n
um
b
er
of
groups
will
it
b
e
able
to
mak
e?
b
Ho
w
man
y
male
and
female
c
horisters
will
there
then
b
e
in
eac
h
group?
E.3455
1
Determine
the
P
GC
D
of
the
in
tegers
75
and
45
.
2
T
w
o
florists
ha
v
e
the
same
sto
c
k
:
45
irises
and
75
roses.
They
eac
h
ha
v
e
their
o
wn
ideas
ab
out
ho
w
to
use
these
flo
w
ers
:
The
florist
A
w
an
ts
to
mak
e
iris
b
ouquets
and
rose
b
ouquets
eac
h
with
the
same
n
um
b
er
of
flo
w
ers.
He
also
w
an
ts
these
b
ouquets
to
ha
v
e
as
man
y
flo
w
ers
as
p
ossible.
The
florist
B
wishes
to
mak
e
the
maxim
um
n
um
b
er
of
b
ouquets
all
iden
tical
where
eac
h
b
ouquet
con
tains
irises
and
roses.
a
Determine
the
n
um
b
er
of
iris
b
ouquets
and
the
n
um
b
er
of
rose
b
ouquets
made
b
y
the
florist
A
.
b
Determine
the
n
um
b
er
of
b
ouquets
of
flo
w
ers
(and
their
c
omp
osition)
made
b
y
the
florist
B
.
E.609
F
or
the
village
fête,
the
patissier
prepared
bags
of
cak
es.
In
some,
he
put
pains
au
c
ho
colat
and
in
others
croissan
ts.
He
put
the
same
n
um
b
er
of
cak
es
in
eac
h
bag.
there
are
a
total
of
910
pains
au
c
ho
colat
and
693
croissan
ts.
1
W
an
ting
to
put
as
man
y
cak
es
as
p
ossible
in
eac
h
pac
k
age,
ho
w
man
y
cak
es
did
he
put
in
eac
h
bag?
2
Ho
w
man
y
bags
con
taining
croissan
ts
are
there?
E.3379
1
Determine
the
GCD
of
120
and
144
using
the
metho
d
of
y
our
c
hoice.
Sho
w
y
our
in
termediate
calculations.
2
A
salesp
erson
has
a
sto
c
k
of
120
b
ottles
of
tiare
p
erfume
and
144
bars
of
monoi
soap.
He
w
an
ts
to
sell
all
of
this
sto
c
k
b
y
making
as
man
y
ˇSouv
enirs
of
P
olynesiaı
gift
sets
as
p
ossible,
suc
h
that
:
the
n
um
b
er
of
b
ottles
of
tiare
p
erfume
is
the
same
in
eac
h
gift
set
;
the
n
um
b
er
of
monoï
soap
bars
is
the
same
in
eac
h
gift
set
;
all
b
ottles
and
soap
bars
are
used.
Find
the
n
um
b
er
of
gift
sets
to
prepare
and
the
con
ten
ts
of
eac
h
one.
The
ev
aluation
of
this
question
will
tak
e
in
to
accoun
t
ob-
serv
ations
and
researc
h
steps,
ev
en
if
incomplete
;
include
them
in
y
our
answ
er.
3
The
algorithm
of
successiv
e
subtractions
can
b
e
used
to
find
the
GCD
of
t
w
o
giv
en
in
tegers.
He
uses
the
follo
wing
prop
ert
y
:
ˇ
a
and
b
b
eing
t
w
o
p
ositiv
e
in
tegers
suc
h
that
a
is
greater
than
b
,
P
GC
D
(
a
;
b
)
=
P
GC
D
(
b
;
a
−
b
)
ı
’
On
a
spreadsheet,
Heiarri
created
this
w
orksheet
to
find
the
P
GC
D
of
2
277
and
1
449
.
A
B
C
1
a
b
a
−
b
2
2277
1449
828
3
1449
828
621
4
828
621
207
5
621
207
414
6
414
207
207
7
207
207
0
a
Using
his
spreadsheet,
sa
y
what
is
the
P
GC
D
of
2.277
and
1.449
.
b
What
form
ula
did
he
write
in
cell
C2
to
obtain
the
result
indicated
in
this
cell
b
y
the
spreadsheet?
E.644
The
two
questions
in
this
exer
cise
ar
e
indep
endent.
6510
blac
k
an
ts
and
4650
red
an
ts
decide
to
join
forces
to
figh
t
termites.
1
T
o
do
this,
the
queen
an
t
w
an
ts
to
form
teams,
using
all
the
an
ts,
whic
h
will
all
b
e
made
up
in
the
same
w
a
y
:
one
n
um
b
er
of
red
an
ts
and
another
n
um
b
er
of
blac
k
an
ts.
What
is
the
maxim
um
n
um
b
er
of
teams
the
queen
can
form
in
this
w
a
y?
2
If
all
the
an
ts,
red
and
blac
k,
stand
in
single
file,
they
form
a
column
42.78
m
long.
Kno
wing
that
a
red
an
t
is
2
mm
longer
than
a
blac
k
an
t,
determine
the
size
of
a
red
an
t
and
a
blac
k
an
t.
E.608
F
or
Ma
y
1
er
,
Julie
has
182
sprigs
of
lily
of
the
v
alley
and
78
roses.
She
w
an
ts
to
mak
e
as
man
y
iden
tical
b
ouquets
as
p
ossible
using
all
her
flo
w
ers.
Ho
w
man
y
iden
tical
b
ouquets
can
she
mak
e?
What
will
b
e
the
comp
osition
of
eac
h
b
ouquet?
h
ttps:/
/c
hingmath.fr
chapExoCorrec/3459
sacados/3459
chapExoCorrec/619
sacados/619
Asie - Juin 2003 - 4 points
chapExoCorrec/3455
sacados/3455
chapExoCorrec/609
sacados/609
Groupe Nord - Septembre 2002 - 2 points
chapExoCorrec/3379
sacados/3379
chapExoCorrec/644
sacados/644
chapExoCorrec/608
sacados/608
Groupe Nord - Juin 2002 - 3 points
9
51
=
÷
÷
9
51
GCF
=
1
72
15
=
÷
÷
72
15
GCF
=
2
56
12
=
÷
÷
56
12
GCF
=
3
15
80
=
÷
÷
15
80
GCF
=
4
5.
PPCM
E.279
In
a
newly
built
house,
w
e
w
an
t
to
tile
the
flo
ors
in
certain
ro
oms.
1
The
kitc
hen
flo
or
is
a
rectangle
of
length
4.55
m
and
width
3.85
m
.
W
e
w
an
t
to
tile
this
ro
om
with
square
tiles,
without
mak-
ing
an
y
cuts
;
furthermore,
the
dimensions
of
these
pa
v
ers
m
ust
b
e
a
whole
n
um
b
er
of
cen
timeters.
a
Giv
e
the
largest
size
of
square
pa
v
ers
that
can
b
e
used
in
these
ro
oms.
b
Giv
e
all
p
ossible
sizes.
2
Rectangular
tiles
of
24
cm
length
and
15
cm
width
are
a
v
ailable.
What
is
the
dimension
of
the
smallest
square
ro
om
that
can
b
e
pa
v
ed
without
an
y
additional
cutting
of
the
slabs?
E.1471
F
or
his
birthda
y
,
P
aul
has
made
a
pizza
measuring
60
cm
long
b
y
24
cm
wide.
He
wishes
to
cut
his
pizza
as
follo
ws
:
Eac
h
part
m
ust
b
e
square
and
of
the
same
size.
The
dimensions
of
a
share
m
ust
b
e
expressed
using
a
whole
n
um
b
er
of
cen
timeters.
Let’s
help
him
c
ho
ose
the
size
of
eac
h
slice.
1
Find
the
eigh
t
divisors
of
the
in
teger
24.
2
Find
the
t
w
elv
e
divisors
of
the
in
teger
60.
3
What
are
the
common
divisors
of
the
in
tegers
24
and
60?
4
Giv
e
the
p
ossible
dimensions
of
eac
h
slice
of
P
aul’s
pizza.
6.
Us-math
:
GCF
E.9637
With
American
notations
:
the
ˇ
greatest
common
fac-
tor
ı
(GCF)
of
t
w
o
in
tegers
is
the
greatest
common
factor.
F
or
example
:
the
factors
of
18
are
:
1
,
2
,
3
,
6
,
9
and
18
factors
of
24
are
:
1
,
2
,
3
,
4
,
6
8
,
12
and
24
Ainsi,
le
GCF
de
18
et
24
est
6
.
F
or
eac
h
question,
complete
the
blanks
:
h
ttps:/
/c
hingmath.fr
chapExoCorrec/279
sacados/279
chapExoCorrec/1471
sacados/1471
chapExoCorrec/9637
sacados/9637
9
51
=
÷
÷
9
51
GCF
=
1
72
15
=
÷
÷
72
15
GCF
=
2
56
12
=
÷
÷
56
12
GCF
=
3
15
80
=
÷
÷
15
80
GCF
=
4
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