Highest Common Factor of 540, 324 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 540, 324 i.e. 108 the largest integer that leaves a remainder zero for all numbers.

HCF of 540, 324 is 108 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 540, 324 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 540, 324 is 108.

HCF(540, 324) = 108

HCF of 540, 324 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 540, 324 is 108.

Highest Common Factor of 540,324 using Euclid's algorithm

Highest Common Factor of 540,324 is 108

Step 1: Since 540 > 324, we apply the division lemma to 540 and 324, to get

540 = 324 x 1 + 216

Step 2: Since the reminder 324 ≠ 0, we apply division lemma to 216 and 324, to get

324 = 216 x 1 + 108

Step 3: We consider the new divisor 216 and the new remainder 108, and apply the division lemma to get

216 = 108 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 108, the HCF of 540 and 324 is 108

Notice that 108 = HCF(216,108) = HCF(324,216) = HCF(540,324) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 540, 324 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 540, 324?

Answer: HCF of 540, 324 is 108 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 540, 324 using Euclid's Algorithm?

Answer: For arbitrary numbers 540, 324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.