Correct Answer - Option 3 : 10
Concept used:
If N be the number whose prime factorization is 2a × qb × rc
Total number of factors (a + 1)(b + 1)(c + 1)
Total number of odd factors are (b +1)(c + 1)
Total number of even factor = total number of factors - odd number of factors
Calculation:
Multiples of 2500 = 52 × 52 × 22
⇒ 54 × 22
Now total number of factors = (4 + 1)(2 + 1)
⇒ 5 × 3
⇒ 15
Odd factors of 2500 = (4 + 1) = 5
Even factors of 2500 = 15 - 5
⇒ 10
∴ The correct answer is 10.
