What is the total number of distinct positive prime factors of the integer 60? — GMAT

What is the total number of distinct positive prime factors of the integer $60$ ?

The total number of distinct positive prime factors of

60

3

To find the number of distinct positive prime factors of

60

, perform prime factorization:

60 = 2^2 \times 3^1 \times 5^1

. The distinct prime numbers in this expression are

2

3

, and

5

. Therefore, there are

3

distinct positive prime factors.

Find the prime factorization of

60

60 = 2^2 \times 3^1 \times 5^1

Expressing the integer as a product of prime numbers reveals all of its prime factors.

Identify the distinct prime bases in the factorization.

The distinct prime factors are

2

3

, and

5

Prime factors are the prime numbers that divide the given integer evenly.

Count the number of distinct prime factors.

There are

3

distinct prime factors.

Counting the elements in the set

\{2, 3, 5\}

gives

3

Prime Factorization and Prime Factors

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