Which of the Factors of 36 are Prime numbers? Explain how you know.

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brettd eNotes educator| Certified Educator

The definition of a prime number is any number that is divisible only by itself and 1.  If I factor out the number 36, I have 1, 2, 3, 4, 6, 9, 12, 18 and 36.  The only numbers in that selection that are only divisible by themselves and 1 are 1, 2, and 3.

Another good way to tell if something is not a prime number is if it is an even number.  The number 2 is the only even number which is also a prime number.  Every other even number is not.  Also, just because a factor is an odd number does not mean it is also a prime.  9 is an example of an odd number that is a factor of 36, but it is also divisible by 3.

hala718 eNotes educator| Certified Educator

Let us factor 36:

36 factors are : 1, 2, 3, 4, 6, 9, 12, 18

Prime numbers are the numbers divisible by 1 and themselves only.

Then prime numbers are: 1, 2, 3.

krishna-agrawala | Student

Factors of a number are the set of numbers that when multiplied together equal the original number.

Every whole number except 1 can be expressed as the product of at least two factors - 1 and itself.

A number that has only two different factors 1 and itself is called a prime number. A number that has any factors other than 1 and itself is called a composite number. Number 1 is neither a prime number nor a composite number.

Factors of a number consisting of only prime numbers are called prime factors.  Each number has only one set of prime numbers. Thus prime factors of number 36 are 2, 2, 3, and 3. Thus:

36 = 2 x 2 x 3 x3

Thus among factors of 36, only 2 and 3 are prime numbers.

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