
Shortcut Trick
Prime factorization of 24 = 23 × 31
Total positive factors = (Power of 2 + 1) × (Power of 3 + 1)
⇒ (3 + 1) × (1 + 1)
⇒ 4 × 2 = 8
∴ The correct answer is 8.

Alternate Method
Given:
The number is 24.
Concept Used:
The positive factors of a number are all the integers that divide the number completely without leaving a remainder.
Calculation:
⇒ Let us list the pairs of positive integers whose product is 24.
⇒ 1 × 24 = 24
⇒ 2 × 12 = 24
⇒ 3 × 8 = 24
⇒ 4 × 6 = 24
⇒ The positive factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
⇒ Counting them gives exactly 8 factors.
∴ The correct answer is 8.

Additional Information
Total Number of Factors
If a number N = pa × qb × rc (where p, q, r are prime factors), then the total number of factors = (a + 1)(b + 1)(c + 1).
Number of Odd Factors
To find odd factors, ignore the powers of 2. For N = 2a × pb × qc (where p, q are odd primes), odd factors = (b + 1)(c + 1).
Number of Even Factors
Subtract the number of odd factors from the total factors, or calculate directly using a × (b + 1)(c + 1).
Sum of Factors
For N = pa × qb, the sum of all factors is [(pa+1 − 1) ÷ (p − 1)] × [(qb+1 − 1) ÷ (q − 1)].