Highest Common Factor of 634, 566 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 634, 566 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 634, 566 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 634, 566 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 634, 566 is 2.

HCF(634, 566) = 2

HCF of 634, 566 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 634, 566 is 2.

Highest Common Factor of 634,566 using Euclid's algorithm

Highest Common Factor of 634,566 is 2

Step 1: Since 634 > 566, we apply the division lemma to 634 and 566, to get

634 = 566 x 1 + 68

Step 2: Since the reminder 566 ≠ 0, we apply division lemma to 68 and 566, to get

566 = 68 x 8 + 22

Step 3: We consider the new divisor 68 and the new remainder 22, and apply the division lemma to get

68 = 22 x 3 + 2

We consider the new divisor 22 and the new remainder 2, and apply the division lemma to get

22 = 2 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 634 and 566 is 2

Notice that 2 = HCF(22,2) = HCF(68,22) = HCF(566,68) = HCF(634,566) .

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Frequently Asked Questions on HCF of 634, 566 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 634, 566?

Answer: HCF of 634, 566 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 634, 566 using Euclid's Algorithm?

Answer: For arbitrary numbers 634, 566 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.