Highest Common Factor of 977, 564 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 977, 564 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 977, 564 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 977, 564 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 977, 564 is 1.

HCF(977, 564) = 1

HCF of 977, 564 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 977, 564 is 1.

Highest Common Factor of 977,564 using Euclid's algorithm

Highest Common Factor of 977,564 is 1

Step 1: Since 977 > 564, we apply the division lemma to 977 and 564, to get

977 = 564 x 1 + 413

Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 413 and 564, to get

564 = 413 x 1 + 151

Step 3: We consider the new divisor 413 and the new remainder 151, and apply the division lemma to get

413 = 151 x 2 + 111

We consider the new divisor 151 and the new remainder 111,and apply the division lemma to get

151 = 111 x 1 + 40

We consider the new divisor 111 and the new remainder 40,and apply the division lemma to get

111 = 40 x 2 + 31

We consider the new divisor 40 and the new remainder 31,and apply the division lemma to get

40 = 31 x 1 + 9

We consider the new divisor 31 and the new remainder 9,and apply the division lemma to get

31 = 9 x 3 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 977 and 564 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(31,9) = HCF(40,31) = HCF(111,40) = HCF(151,111) = HCF(413,151) = HCF(564,413) = HCF(977,564) .

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Frequently Asked Questions on HCF of 977, 564 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 977, 564?

Answer: HCF of 977, 564 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 977, 564 using Euclid's Algorithm?

Answer: For arbitrary numbers 977, 564 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.