SOLUTION: Determine the total number of divisors of the number 5880. How many are even? How many are odd?

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Question 1201254: Determine the total number of divisors of the number 5880. How many are even? How many are odd?
Answer by greenestamps(13198) (Show Source):
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Find the prime factorization....

5880
588*10
4*147*2*5
2*2*7*21*2*5
2*2*7*7*3*2*5

The prime factorization is (2^3)(3^1)(5^1)(7^2).

To find the total number of divisors, add 1 to each of the exponents in the prime factorization and multiply those numbers. The total number of divisors is 4*2*2*3 = 48.

The odd divisors are those that do not contain any factor of 2. To find the number of odd divisors, add 1 to each of the exponents of an odd prime factor and multiply those numbers. The number of odd divisors is 2*2*3 = 12.

ANSWERS:
total number of divisors: 48
number of odd divisors: 12
number of even divisors: 48-12 = 36