Question

How many positive integers less than 100 have a remainder of 3 when divided by 7?

Answer 1

Answer:

the answer is 3, 10, 17, 94

Answer 2

14 positive Integers

To have a remainder of
3
when divided by
7
, an integer must be
3
more than a multiple of
7
. For example, when
73
is divided by
7
, the quotient is
10
and the remainder is
3
:
73

=
10

×
7

+
3
. Just take the multiples of
7
and add
3
:

0
_

×
7

+
3

=
3
;
1
_

×
7

+
3

=
10
;
2
_

×
7

+
3

=
17
;
…
;
13
_

×
7

+
3

=
94

There are
14
positive integers less than
100
that have a remainder of
3
when divided by
7
. If
a
and
b
are integers, the following four terms are synonymous:

a
is a divisor of
b
.
a
is a factor of
b
.

b
is divisible by
a
.
b
is a multiple of
a
.
All these statements mean that, when
b
is divided by
a
, there is no remainder (or, more precisely, the remainder is
0
). For example:

3
is a divisor of
12
.
3
is a factor of
12
.

12
is divisible by
3
.
12
is a multiple of
3
.