Highest Common Factor of 687, 916 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 687, 916 i.e. 229 the largest integer that leaves a remainder zero for all numbers.

HCF of 687, 916 is 229 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 687, 916 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 687, 916 is 229.

HCF(687, 916) = 229

HCF of 687, 916 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 687, 916 is 229.

Highest Common Factor of 687,916 using Euclid's algorithm

Highest Common Factor of 687,916 is 229

Step 1: Since 916 > 687, we apply the division lemma to 916 and 687, to get

916 = 687 x 1 + 229

Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 229 and 687, to get

687 = 229 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 229, the HCF of 687 and 916 is 229

Notice that 229 = HCF(687,229) = HCF(916,687) .

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Frequently Asked Questions on HCF of 687, 916 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 687, 916?

Answer: HCF of 687, 916 is 229 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 687, 916 using Euclid's Algorithm?

Answer: For arbitrary numbers 687, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.