# Highest Common Factor of 72, 274 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 72, 274 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 72, 274 is 2 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 72, 274 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 72, 274 is 2.

HCF(72, 274) = 2

## HCF of 72, 274 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 72, 274 is 2. ### Highest Common Factor of 72,274 is 2

Step 1: Since 274 > 72, we apply the division lemma to 274 and 72, to get

274 = 72 x 3 + 58

Step 2: Since the reminder 72 ≠ 0, we apply division lemma to 58 and 72, to get

72 = 58 x 1 + 14

Step 3: We consider the new divisor 58 and the new remainder 14, and apply the division lemma to get

58 = 14 x 4 + 2

We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 72 and 274 is 2

Notice that 2 = HCF(14,2) = HCF(58,14) = HCF(72,58) = HCF(274,72) .

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### Frequently Asked Questions on HCF of 72, 274 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 72, 274?

Answer: HCF of 72, 274 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 72, 274 using Euclid's Algorithm?

Answer: For arbitrary numbers 72, 274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.