Highest Common Factor of 637, 817 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, 817 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 637, 817 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, 817 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, 817 is 1.

HCF(637, 817) = 1

HCF of 637, 817 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, 817 is 1.

Highest Common Factor of 637,817 using Euclid's algorithm

Highest Common Factor of 637,817 is 1

Step 1: Since 817 > 637, we apply the division lemma to 817 and 637, to get

817 = 637 x 1 + 180

Step 2: Since the reminder 637 ≠ 0, we apply division lemma to 180 and 637, to get

637 = 180 x 3 + 97

Step 3: We consider the new divisor 180 and the new remainder 97, and apply the division lemma to get

180 = 97 x 1 + 83

We consider the new divisor 97 and the new remainder 83,and apply the division lemma to get

97 = 83 x 1 + 14

We consider the new divisor 83 and the new remainder 14,and apply the division lemma to get

83 = 14 x 5 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 637 and 817 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(83,14) = HCF(97,83) = HCF(180,97) = HCF(637,180) = HCF(817,637) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 637, 817 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, 817?

Answer: HCF of 637, 817 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 637, 817 using Euclid's Algorithm?

Answer: For arbitrary numbers 637, 817 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.