Question

The prime factorization of integer N is A x A x B x C, where A, B and C are all distinct prime
integers. How many factors does N have?
A. 12
B. 24
C. 4
D. 6

Answer 1

Start with the number N itself and 1.
That's 2 factors.

Answer 2

Now find all distinct 1-factor combinations, 2-factor combinations, and 3-factor combinations.

Answer 3

How many distinct products of two factors are there?

Answer 4

AA, AB, AC, BC
That's 4 more factors of N.

Answer 5

How many distinct products of three factors are there?
AAB, AAC, ABC
That's 3 more factors of N.

Answer 6

Finally, how many distinct 1-prime-factor factors of N are there?
A, B, C
That's 3 more factors of N.

Now add them up.

Answer 7

Thank u :)

Answer 8

You're welcome.