How many positive integer factors of 36 are prime numbers? — GRE General Test

How many positive integer factors of $36$ are prime numbers?

There are

2

positive integer factors of

36

that are prime numbers:

2

and

3

Listing all positive integer factors of

36

yields

1, 2, 3, 4, 6, 9, 12, 18,

and

36

. Evaluating each factor against the definition of a prime number (an integer greater than

1

divisible only by

1

and itself) shows that only

2

and

3

are prime. Therefore, there are exactly

2

prime factors.

Find all positive integer factors of

36

The positive integer factors of

36

are

1, 2, 3, 4, 6, 9, 12, 18,

and

36

Dividing

36

by integers from

1

36

yields integer quotients for these nine numbers.

Identify which of these factors meet the definition of a prime number.

The prime factors are

2

and

3

A prime number is an integer greater than

1

with exactly two distinct positive divisors:

1

and itself. The integer

1

is not prime, while

4, 6, 9, 12, 18,

and

36

are composite.

Count the identified prime factors.

The total count is

2

There are exactly two distinct prime numbers (

2

and

3

) in the list of factors.

Prime Factors and Definition of Prime Numbers

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