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3
2
1
Grade 8
/ Arithmetic
16 exercises (100% corrected)
a
Number of divisors
(5 exercices)
First integers
(3 exercices)
Decomposition of an integer into a product of prime numbers
(5 exercices)
Simplification of fractions
(3 exercices)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
r
2
9
8
-
1
r
1
1
4
-
0
1.
Numb
er
of
divisors
E.9073
Definition
:
Let
a
and
b
b
e
t
w
o
p
ositiv
e
in
tegers.
W
e
sa
y
that
b
is
a
divisor
of
the
n
um
b
er
a
if
there
exists
an
in
teger
k
suc
h
that
:
a
=
k
×
b
1
If
p
ossible,
complete
the
dotted
lines
b
elo
w
using
in
te-
gers
:
a
18
=
1
×
:
:
:
b
18
=
2
×
:
:
:
c
18
=
3
×
:
:
:
d
18
=
4
×
:
:
:
e
18
=
5
×
:
:
:
f
18
=
6
×
:
:
:
g
18
=
7
×
:
:
:
h
18
=
8
×
:
:
:
i
18
=
9
×
:
:
:
2
Giv
e
the
set
of
divisors
of
the
n
um
b
er
18
.
E.9074
a
Giv
e
the
2
factors
of
the
n
um
b
er
13
.
b
Giv
e
the
6
factors
of
the
n
um
b
er
12
.
c
Giv
e
the
4
factors
of
the
in
teger
22
.
E.9075
1
a
Giv
e
all
divisors
of
the
in
teger
8
.
b
Giv
e
all
divisors
of
the
in
teger
9
.
2
Giv
e
the
12
divisors
of
the
in
teger
8
×
9
.
E.9322
Sa
y
whether
the
follo
wing
statemen
t
is
true
or
false
:
Assertion
:
for
all
in
tegers
n
b
et
w
een
2
and
9
,
2
n
−
1
is
a
prime
n
um
b
er.
E.9326
Determine
the
smallest
o
dd
p
ositiv
e
in
teger
that
has
three
differen
t
prime
factors.
Ex-
plain
y
our
reasoning.
2.
First
inte
gers
E.9076
The
table
b
elo
w
sho
ws
the
in
tegers
from
2
to
99
:
1
a
Circle
the
in
teger
2
.
b
Hash
the
b
o
xes
whose
in
teger
admits
2
as
a
factor.
2
a
Circle
the
in
teger
3
.
b
Hash
the
b
o
xes
whose
in
teger
admits
3
as
a
factor.
3
a
Rep
eat
the
previous
instructions
with
the
in
tegers
5
and
7
.
b
Circle
all
of
the
nonhidden
n
um
b
ers
on
the
grid.
4
a
Ho
w
man
y
factors
do
the
in
tegers
2
,
3
,
5
,
7
,
11
ad-
mit?
b
Whic
h
of
the
in
tegers
13
,
17
,
19
,
23
,
29
,
31
,
37
,
41
,
47
,
b
elong
to
a
m
ultiplication
table?
If
so,
whic
h
one?
c
F
or
what
reason
can
w
e
sa
y
that
the
n
um
b
er
97
admits
only
t
w
o
factors
1
and
97
?
Definition
:
an
in
teger
a
is
said
to
b
e
prime
if
it
admits
exactly
2
factors
:
1
and
itself.
Example
:
the
in
tegers
2
,
3
,
5
,
7
,
11
,
13
are
prime
in
tegers.
Note
:
this
exercise
in
tro
duces
the
so-called
ˇ
siev
e
metho
d
of
Eratosthène
ı
for
quic
kly
determining
the
prime
in
tegers
among
2
to
99
.
Eratosthenes
w
as
a
Greek
scien
tist
of
the
2
e
cen
tury
BC.
He
is
kno
wn
for
b
eing
app
oin
ted
director
of
the
library
of
Alexandria
and
for
b
eing
the
first
to
measure
the
circumference
of
the
Earth.
A
slide
sho
w
featuring
the
Eratosthenes
siev
e
can
b
e
found
in
the
link
to
the
righ
t.
E.9077
1
Whic
h
of
the
follo
wing
in
tegers
is
not
a
prime
in
teger
:
31
;
33
;
37
;
41
2
Whic
h
of
the
follo
wing
is
not
a
prime
in
teger
:
43
;
47
;
49
;
53
In
the
link
to
the
righ
t
y
ou
will
find
the
list
of
prime
in
tegers
less
than
or
equal
to
1
000
.
E.9078
Eac
h
of
the
statemen
ts
b
elo
w
is
false.
F
or
eac
h
of
these
statemen
ts,
find
a
coun
terexample
to
dis-
pro
v
e
it
:
1
The
sum
of
t
w
o
prime
in
tegers
is
a
prime
in
teger.
2
The
m
ultiplication
of
t
w
o
prime
in
tegers
is
a
prime
in
te-
ger.
3
All
o
dd
in
tegers
are
prime
in
tegers.
3.
De
c
omp
osition
of
an
inte
ger
into
a
pr
o
duct
of
prime
numb
ers
h
ttps:/
/c
hingmath.fr
chapExoCorrec/9073
sacados/9073
chapExoCorrec/9074
sacados/9074
chapExoCorrec/9075
sacados/9075
chapExoCorrec/9322
sacados/9322
chapExoCorrec/9326
sacados/9326
chapExoCorrec/9076
sacados/9076
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
r
2
9
8
-
1
chapExoCorrec/9077
sacados/9077
r
1
1
4
-
0
chapExoCorrec/9078
sacados/9078
72
2
×
36
72
2
×
2
×
18
72
2
×
2
×
2
×
9
72
2
×
2
×
2
×
3
×
3
E.9079
Definition
:
an
in
teger
is
said
to
b
e
decomp
osed
in
to
a
pro
duct
of
prime
in
tegers
if
it
is
written
as
a
pro
duct
whose
factors
are
all
prime
in
tegers.
Example
:
the
in
teger
72
admits
the
decomp
osition
:
2
×
2
×
2
×
3
×
3
Algorithm
:
opp
osite
is
a
metho
d
of
obtaining
the
decomp
osition
of
an
in
te-
ger
in
to
a
pro
duct
of
prime
in
tegers
:
1
Use
the
equalit
y
28
=
2
×
14
to
obtain
the
prime
pro
duct
decomp
osition
of
the
in
teger
28
.
2
Use
equalit
y
40
=
2
×
20
to
obtain
the
prime
pro
duct
de-
comp
osition
of
the
in
teger
40
.
3
Use
equalit
y
96
=
2
×
48
to
obtain
the
prime
pro
duct
de-
comp
osition
of
the
in
teger
96
.
E.9080
F
or
eac
h
of
the
in
tegers
198
,
297
,
462
,
determine
their
decomp
osition
in
to
a
pro
duct
of
primes.
Hin
ts
:
for
this,
use
the
equalities
:
198
=
6
×
33
297
=
9
×
33
462
=
14
×
33
E.9081
1
Justify
that
the
n
um
b
er
102
is
divisible
b
y
3
.
2
Decomp
ose
102
in
to
pro
ducts
of
prime
factors.
3
Giv
e
3
nonprime
factors
of
the
n
um
b
er
102
.
E.9321
What
is
the
largest
prime
n
um
b
er
that
divides
41
895
?
E.9324
1
a
Determine
the
prime
factor
pro
duct
decomp
osition
of
2744
.
b
Determine
the
prime
factor
pro
duct
decomp
osition
of
2744
2
.
c
Using
this
decop
osition,
find
x
suc
h
that
:
x
3
=
2744
2
2
Let
a
and
b
b
e
t
w
o
in
tegers
greater
than
2
suc
h
that
:
a
3
=
b
2
a
Calculate
b
when
a
=
100
.
b
Determine
t
w
o
in
tegers
a
and
b
greater
than
2
and
less
than
10
that
v
erify
the
equalit
y
a
3
=
b
2
.
4.
Simplific
ation
of
fr
actions
E.9082
1
Giv
e
the
pro
duct
decomp
osition
of
the
prime
in
tegers
of
the
in
tegers
:
42
;
90
2
Deriv
e
the
reduced
writing
of
the
fraction
42
90
.
E.9083
1
Decomp
ose
140
and
870
in
to
the
pro
duct
of
primes.
2
Deduce
the
irreducible
form
of
the
fraction
140
870
E.9084
1
Decomp
ose,
without
justification,
the
n
um
b
ers
1
386
and
1
716
in
to
pro
ducts
of
prime
factors.
2
Deduce
the
irreducible
form
of
the
fraction
:
1
386
1
716
h
ttps:/
/c
hingmath.fr
chapExoCorrec/9079
sacados/9079
72
2
×
36
72
2
×
2
×
18
72
2
×
2
×
2
×
9
72
2
×
2
×
2
×
3
×
3
chapExoCorrec/9080
sacados/9080
chapExoCorrec/9081
sacados/9081
chapExoCorrec/9321
sacados/9321
chapExoCorrec/9324
sacados/9324
chapExoCorrec/9082
sacados/9082
chapExoCorrec/9083
sacados/9083
chapExoCorrec/9084
sacados/9084
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