Find the total number of positive factors of the integer 75. — State PSC Exam

Find the total number of positive factors of the integer $75$ .

Answer: 6

The total number of positive factors of 75 is 6.

The prime factorization of 75 is

3^1 \times 5^2

. The number of positive factors is obtained by adding 1 to each exponent in the prime factorization and multiplying the results:

(1 + 1) \times (2 + 1) = 2 \times 3 = 6

. The complete list of positive factors is 1, 3, 5, 15, 25, and 75.

Express 75 in terms of its prime factors.

75 = 3^1 \times 5^2

Prime factorization breaks down the number into prime components essential for counting factors.

Apply the standard formula for total positive factors of a number

N = p^a \times q^b

Total factors

= (1 + 1) \times (2 + 1) = 2 \times 3 = 6

Each factor is formed by choosing a power of 3 (2 choices:

3^0, 3^1

) and a power of 5 (3 choices:

5^0, 5^1, 5^2

Total Number of Positive Factors from Prime Factorization

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