# Highest Common Factor of 60, 84, 108 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 60, 84, 108 i.e. 12 the largest integer that leaves a remainder zero for all numbers.

HCF of 60, 84, 108 is 12 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 60, 84, 108 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 60, 84, 108 is 12.

HCF(60, 84, 108) = 12

## HCF of 60, 84, 108 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 60, 84, 108 is 12. ### Highest Common Factor of 60,84,108 is 12

Step 1: Since 84 > 60, we apply the division lemma to 84 and 60, to get

84 = 60 x 1 + 24

Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 24 and 60, to get

60 = 24 x 2 + 12

Step 3: We consider the new divisor 24 and the new remainder 12, and apply the division lemma to get

24 = 12 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 60 and 84 is 12

Notice that 12 = HCF(24,12) = HCF(60,24) = HCF(84,60) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 108 > 12, we apply the division lemma to 108 and 12, to get

108 = 12 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 12 and 108 is 12

Notice that 12 = HCF(108,12) .

### HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

### Frequently Asked Questions on HCF of 60, 84, 108 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 60, 84, 108?

Answer: HCF of 60, 84, 108 is 12 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 60, 84, 108 using Euclid's Algorithm?

Answer: For arbitrary numbers 60, 84, 108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.