# Highest Common Factor of 54, 72 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 54, 72 i.e. 18 the largest integer that leaves a remainder zero for all numbers.

HCF of 54, 72 is 18 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 54, 72 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 54, 72 is 18.

HCF(54, 72) = 18

## HCF of 54, 72 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 54, 72 is 18. ### Highest Common Factor of 54,72 is 18

Step 1: Since 72 > 54, we apply the division lemma to 72 and 54, to get

72 = 54 x 1 + 18

Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 18 and 54, to get

54 = 18 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 54 and 72 is 18

Notice that 18 = HCF(54,18) = HCF(72,54) .

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### Frequently Asked Questions on HCF of 54, 72 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 54, 72?

Answer: HCF of 54, 72 is 18 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 54, 72 using Euclid's Algorithm?

Answer: For arbitrary numbers 54, 72 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.