Question

There are many numbers that divide 109 with a remainder of 4. List all two-digit numbers that have that property.

Answer 1

15, 21, &35

Explanation:

109-4=105

Factorize 105:

1x105

3x35

5x21

7x15

1, 3, 5, & 7 are all one digits numbers and 105 is a three digit number.

The 3 two digit numbers are 15, 21, & 35.

Answer 2

3 Numbers: 15, 21, 35

Explanation:

We want number that divide 109 with a remainder of 4.

Thus, it can divide of 109 - 4 = 105

Factors of 105 = 3, 5, 7

Thus for getting two digit number it must be Multiple of any two factors of 105.

i.e. 15, 21 and 35

Hence there are only 3 numbers that divide 109 with a remainder of 4.