Solution:

Number 75,600 can be factorized as follows:

75,600 = 2^4 × 3^2 × 5^2 × 7

The number of factors can be calculated by using the formula:

Number of factors = (a+1) × (b+1) × (c+1)...(where a, b, c are the powers of prime factors)

Therefore, the number of factors of 75,600 can be calculated as:

(4+1) × (2+1) × (2+1) × (1+1) = 5 × 3 × 3 × 2 = 90

However, this includes the factor 1 and the number itself (75,600), so the actual number of different factors is:

90 - 2 = 88

Therefore, the correct answer is (d) none of these.

Explanation:

The number of factors of a given number is calculated by finding all the possible combinations of its prime factors. The formula for calculating the number of factors of a given number is based on the powers of prime factors.

In this question, we have factorized the given number into its prime factors and used the formula to calculate the number of factors. However, we need to subtract 2 from the answer as it includes the factors 1 and the number itself.

Hence, the correct answer is (d) none of these, as none of the options match with the calculated answer.

75600÷120=630 so it's different factors is (a) 120