Highest Common Factor of 760, 722 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 760, 722 i.e. 38 the largest integer that leaves a remainder zero for all numbers.

HCF of 760, 722 is 38 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 760, 722 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 760, 722 is 38.

HCF(760, 722) = 38

HCF of 760, 722 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 760, 722 is 38.

Highest Common Factor of 760,722 using Euclid's algorithm

Highest Common Factor of 760,722 is 38

Step 1: Since 760 > 722, we apply the division lemma to 760 and 722, to get

760 = 722 x 1 + 38

Step 2: Since the reminder 722 ≠ 0, we apply division lemma to 38 and 722, to get

722 = 38 x 19 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 38, the HCF of 760 and 722 is 38

Notice that 38 = HCF(722,38) = HCF(760,722) .

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Frequently Asked Questions on HCF of 760, 722 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 760, 722?

Answer: HCF of 760, 722 is 38 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 760, 722 using Euclid's Algorithm?

Answer: For arbitrary numbers 760, 722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.