Highest Common Factor of 637, 20556 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 637, 20556 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 637, 20556 is 1 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 637, 20556 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 637, 20556 is 1.

HCF(637, 20556) = 1

HCF of 637, 20556 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 637, 20556 is 1.

Highest Common Factor of 637,20556 using Euclid's algorithm

Highest Common Factor of 637,20556 is 1

Step 1: Since 20556 > 637, we apply the division lemma to 20556 and 637, to get

20556 = 637 x 32 + 172

Step 2: Since the reminder 637 ≠ 0, we apply division lemma to 172 and 637, to get

637 = 172 x 3 + 121

Step 3: We consider the new divisor 172 and the new remainder 121, and apply the division lemma to get

172 = 121 x 1 + 51

We consider the new divisor 121 and the new remainder 51,and apply the division lemma to get

121 = 51 x 2 + 19

We consider the new divisor 51 and the new remainder 19,and apply the division lemma to get

51 = 19 x 2 + 13

We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get

19 = 13 x 1 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 637 and 20556 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(51,19) = HCF(121,51) = HCF(172,121) = HCF(637,172) = HCF(20556,637) .

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Frequently Asked Questions on HCF of 637, 20556 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 637, 20556?

Answer: HCF of 637, 20556 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 637, 20556 using Euclid's Algorithm?

Answer: For arbitrary numbers 637, 20556 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.