Let us write the factors of 100. A factor of 100 can only be a multiple of five if it is divisible by five.
- Divisibility rule of 5: A number can only be divisible by five if the ones digit of the number is a five or 0.
Factors of 100 ⇒ numbers divisible by 100 ⇒ 1, 2, 4, 5, 10, 20, 25, 50, 100
When checking each factor of 100;
- 1 is not a multiple of 5 ⇔ not divisible by 5.
- 2 is not a multiple of 5 ⇔ not divisible by 5.
- 4 is not a multiple of 5 ⇔ not divisible by 5.
- 5 is a multiple of 5 ⇔ divisible by 5.
- 10 is a multiple of 5 ⇔ divisible by 5.
- 20 is a multiple of 5 ⇔ divisible by 5.
- 50 is a multiple of 5 ⇔ divisible by 5.
- 100 is a multiple of 5 ⇔ divisible by 5.
⇒ Five factors are multiples of 5.
Therefore, five factors of 100 are multiples of 5.