Question

How many positive integer factors of 100 are multiples of 2 or 3?

Answer 1

Answer:

• 6

Explanation:

The prime factorization of 100 is ...

... 100 = 2²×5²

The exponents of these factors are 2 and 2. Adding 1 to each of them and finding the product of those sums, we have ...

... (2+1)×(2+1) = 9

The number of divisors of 100 is 9. They are ...

... 1, 2, 4, 5, 10, 20, 25, 50, 100

Of these, 2, 4, 10, 20, 50, 100 are divisible by 2. That is, 6 factors of 100 are multiples of 2.

There are no multiples of 3 that are factors of 100, since 3 is not one of the prime factors.