Highest Common Factor of 647, 977 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 647, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 647, 977 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 647, 977 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 647, 977 is 1.

HCF(647, 977) = 1

HCF of 647, 977 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 647, 977 is 1.

Highest Common Factor of 647,977 using Euclid's algorithm

Highest Common Factor of 647,977 is 1

Step 1: Since 977 > 647, we apply the division lemma to 977 and 647, to get

977 = 647 x 1 + 330

Step 2: Since the reminder 647 ≠ 0, we apply division lemma to 330 and 647, to get

647 = 330 x 1 + 317

Step 3: We consider the new divisor 330 and the new remainder 317, and apply the division lemma to get

330 = 317 x 1 + 13

We consider the new divisor 317 and the new remainder 13,and apply the division lemma to get

317 = 13 x 24 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 647 and 977 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(317,13) = HCF(330,317) = HCF(647,330) = HCF(977,647) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 647, 977 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 647, 977?

Answer: HCF of 647, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 647, 977 using Euclid's Algorithm?

Answer: For arbitrary numbers 647, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.