**Definition of Highest Common Factor (HCF)**

- The Highest Common Factor (HCF) of two or more numbers is the highest number that divides the numbers exactly.

**More about Highest Common Factor (HCF)**

- If the highest common factor (HCF) of two numbers is equal to 1, then they are called co-prime or relatively prime.
- The product of the highest common factor (HCF) and the lowest common multiple (LCM) of two numbers is equal to the product of the numbers.

**Example of Highest Common Factor (HCF)**

- To find the HCF of 12, 24, and 36, first we list out the factors of the three numbers.

12 – 1, 2, 3, 4, 6, and**12**

24 – 1, 2, 3, 4, 6, 8,**12**, and 24

36 - 1, 2, 3, 4, 6, 8,**12**, 18, and 36

So, the HCF of the numbers 12, 24, and 36 is 12. - In another method we need to write all the prime factors of the three numbers 12, 24, and 36.

12 – 2 × 2 × 3

24 – 2 × 2 × 2 × 3

36 - 2 × 2 × 3 × 3

Then we list out all the common prime factors. The common prime factors of the three numbers are 2 × 2 × 3.

Then we have to multiply the common prime factors.

2 × 2 × 3 = 12

So, the HCF of the three numbers 12, 24, and 36 is 12.

**Solved Example on Highest Common Factor (HCF)**

Find the HCF of 18 and 35.

Choices:

A. 1

B. 5

C. 7

D. 9

Correct Answer: A

Solution:

Step 1:18 = 1, 2, 3, 6, 9, and 18 [List the factors of 18.]

Step 2:35 = 1, 5, 7, and 35 [List the factors of 35.]

Step 3:The common factor of 18 and 35 is 1.

Step 4:So, the HCF of 18 and 35 is 1.

**Related Terms for Highest Common Factor (HCF)**

- Common Factor
- Factor
- Number
- Prime Factorization