How many of the factors of 900 have exactly 18 factors?

Answer 1

180, 450 and 300

Answer 2

Factors of 900 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900

180 has 18 (1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 38, 45, 60, 90, 180)

300 has 18 (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300)

That's it, 2 of them

Answer 3

Oh, what a happy little question! To find the factors of a number, we first need to find its prime factorization. The prime factorization of 900 is 2^2 * 3^2 * 5^2. To have exactly 18 factors, the number must be in the form p^17 or p^1 * q^2, where p and q are distinct prime numbers. So, the factors of 900 that have exactly 18 factors are numbers of the form 2^17, 3^17, 5^17, 2 * 3^2, 2 * 5^2, and 3 * 5^2.