Highest Common Factor of 671, 776 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 671, 776 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 671, 776 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 671, 776 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 671, 776 is 1.

HCF(671, 776) = 1

HCF of 671, 776 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 671, 776 is 1.

Highest Common Factor of 671,776 using Euclid's algorithm

Highest Common Factor of 671,776 is 1

Step 1: Since 776 > 671, we apply the division lemma to 776 and 671, to get

776 = 671 x 1 + 105

Step 2: Since the reminder 671 ≠ 0, we apply division lemma to 105 and 671, to get

671 = 105 x 6 + 41

Step 3: We consider the new divisor 105 and the new remainder 41, and apply the division lemma to get

105 = 41 x 2 + 23

We consider the new divisor 41 and the new remainder 23,and apply the division lemma to get

41 = 23 x 1 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 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 671 and 776 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(41,23) = HCF(105,41) = HCF(671,105) = HCF(776,671) .

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Frequently Asked Questions on HCF of 671, 776 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 671, 776?

Answer: HCF of 671, 776 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 671, 776 using Euclid's Algorithm?

Answer: For arbitrary numbers 671, 776 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.