Highest Common Factor of 764, 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 764, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 764, 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 764, 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 764, 977 is 1.

HCF(764, 977) = 1

HCF of 764, 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 764, 977 is 1.

Highest Common Factor of 764,977 using Euclid's algorithm

Highest Common Factor of 764,977 is 1

Step 1: Since 977 > 764, we apply the division lemma to 977 and 764, to get

977 = 764 x 1 + 213

Step 2: Since the reminder 764 ≠ 0, we apply division lemma to 213 and 764, to get

764 = 213 x 3 + 125

Step 3: We consider the new divisor 213 and the new remainder 125, and apply the division lemma to get

213 = 125 x 1 + 88

We consider the new divisor 125 and the new remainder 88,and apply the division lemma to get

125 = 88 x 1 + 37

We consider the new divisor 88 and the new remainder 37,and apply the division lemma to get

88 = 37 x 2 + 14

We consider the new divisor 37 and the new remainder 14,and apply the division lemma to get

37 = 14 x 2 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 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 764 and 977 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(37,14) = HCF(88,37) = HCF(125,88) = HCF(213,125) = HCF(764,213) = HCF(977,764) .

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Frequently Asked Questions on HCF of 764, 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 764, 977?

Answer: HCF of 764, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 764, 977 using Euclid's Algorithm?

Answer: For arbitrary numbers 764, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.