What is the total number of positive integer factors of 120? — State PSC Exam

What is the total number of positive integer factors of $120$ ?

Answer: 16

The total number of positive integer factors of

120

16

By prime factorizing

120

, we get

2^3 \times 3^1 \times 5^1

. Applying the factor count formula

(a+1)(b+1)(c+1)

, we obtain

(3+1)(1+1)(1+1) = 4 \times 2 \times 2 = 16

Find the prime factorization of

120

120 = 2^3 \times 3^1 \times 5^1

To calculate the total number of factors systematically, express the number as a product of prime factors.

Apply the total factor count formula

Number of factors =

(3 + 1)(1 + 1)(1 + 1)

If a number

N = p^a \times q^b \times r^c

, the total number of positive factors is

(a+1)(b+1)(c+1)

Compute the product

4 \times 2 \times 2 = 16

Multiplying the incremented prime exponents gives the total count of factors.

Number of Positive Factors from Prime Factorization

Question