Factors of 15 are the whole numbers that can divide the original number, completely. There are four factors of 15, i.e, 1, 3, 5 and 15. Hence, the smallest factor is 1 and the greatest factor of 15 is 15, itself. The sum of all factors of 15 is equal to 24.

Pair factors of 15 are the integers that give the original number 15 when multiplied together in pairs. They are (1, 15) and (3, 5). In this article, we will learn to find the factors of 15 and the prime factorisation of 15 along with examples. 

What are the Factors of 15?

Factors of 15 divide the original number, wholly. A number or an integer that divides 15 evenly without leaving a remainder, then the number is a factor of 15. As the number 15 is an odd composite number, it has more than two factors. Thus, the factors of 15 are 1, 3, 5 and 15.

Pair Factors Of 15

We can find the pair factors of 15, by multiplying two numbers in a pair to get the result as 15, such as:

1 × 15 = 15

3 × 5 = 15

Therefore, the pair factors of 15 are (1, 15) and (3, 5).

How to Find Factors of 15?

15 is a two-digit odd number, thus it is not completely divisible by any even number.

• Divide 15 by 1, to get: 15/1 = 15 and also 15/15 =1 (So, 1 and 15 are the two factors of 15)
• Divide 15 by 3, to get: 15/3 = 5 and also 15/5 = 3 (So, 3 and 5 are the factors of 15)

Thus, the maximum factors we can get here are four, i.e., 1, 3, 5 and 15. Therefore, the factors of 15 are 1, 3, 5 and 15

Prime Factorisation of 15

By prime factorisation of 15, we will get the prime numbers or prime factors, that evenly divides 15. Since 15 is a composite number, thus it is divisible by one or more prime numbers. Now let us find the prime factor of 15.

• Since 15 is an odd number, thus it is not divisible by prime number 2, hence we will divide it by the next prime number, i.e., 3

15 ÷ 3 = 5

• Again divide 5 by 3.

          5 ÷ 3 = 1.67, which is a fraction number.

         Therefore, proceed to the next prime number, i.e. 5.

• Divide 5 by 5.

5 ÷ 5 = 1

• We have received 1 at the end and further, we cannot proceed with the division method. So, the prime factorization of 15 is 3 × 5, where 3 and 5 both are prime numbers.

Factor Tree for 15

The prime factorisation of 15 will result in the prime factors that divide the original evenly. The factor tree for 15 hence can be represented as shown below:

Facts – Factors of 15

• Factors of 15: 1, 3, 5 and 15
• Pair Factors of 15: (1, 15), and (3, 5)
• Prime Factorisation of 15: 3 × 5
• Prime Factors of 15: 3 and 5
• Sum of Factors of 15 = 24

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Solved Examples on Factors of 15

Q.1: What are the common factors of 15 and 16?

Solution: Let us write the factors of 15 and 16.

The factors of 15 are: 1, 3, 5, 15

The factors of 16 are: 1, 2, 4, 8, 16

From the above two lists, we can see the only common factor between 15 and 16 is 1.

Q.2: What is the greatest common factor of 15 and 20?

Solution:

The factors of 15 are: 1, 3, 5, 15

The factors of 20 are: 1, 2, 4, 5, 10, 20

Hence, the highest common factor of 15 and 20 is 5.

Q.3: What is the GCD of 15 and 30?

Solution: GCD stands for the greatest common divisor.

The factors of 15 are: 1, 3, 5, 15

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Hence, the GCD of 15 and 30 is 15.

Practise Questions on Factors of 15

1. How can Ron distribute 15 chocolates among his 5 friends?
2. What is the product of factors of 15, other than 1 and 15?
3. Is 15 a factor of 45?

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