Factors of 15 – Prime factorisation

What do you mean by factors of 15?

When a number divides 15 with 0 remainders, then that number is known as a factor of 15. 

Every number has at least two factors. These two are:

1. 1
2. The number itself i.e., 15

If a number has any factors other than the number itself and 1, then the number is a composite number.

If a number has only two factors, then the number is a prime number. 

Then we have to find out the possible pairs of Integers whose product is 15. These pairs of numbers are known as factors pairs. 

1^{\text {st }}possible way: 15 = 1 × 15

2^{\text {nd}} possible way: 15 = 3 × 5

Since 15 has 4 factors, it is a composite number. The four factors are  1, 15, 3 and 5.

Out of these factors, 3 and 5 are prime numbers and hence are called prime factors of 15.

Note:
We can also write 15 as 2 × 7.5.
But since 7.5 is not an integer, 2 and 7.5 cannot be factors of 15.

Finding factors of 15 by prime factorization

In this method, we have to start dividing the number with the smallest prime divisor till we get 1. 

1. Since 15 is an odd number, it is not divisible by 2. So, we have to start with the next possible prime divisor of 15 which gives 0 remainders.
   Here we start with 3

2. We have to divide the numbers till we get 1 as the last quotient.

Now divide 5 by its smallest prime divisor with 0 remainders.

So we divide 5 by 5.

3 We got 1 on the right-hand side of the table. Now, we can end the prime factorization here.
3 and 5 are the two prime factors of 15.

4. Here we can see that the number 15 can be expressed as a product of two integers in two possible ways.

1^{\text {st }}possible way: 15 = 1 × 15

2^{\text {nd}}possible way: 15 = 3 × 5

5. Therefore, it can be concluded that the composite number 15 has 4 factors that are 1,3,5 and 15. 

Interesting facts about factors

1. 1 is a factor of every number.
2. Every number is a factor of itself.
3. Every factor divides the number exactly with no remainder.
4. The factor of a number can never be greater than the number. It is always less than or equal to that given number.
5. The number of factors of a given number is finite.