Highest Common Factor of 671, 751 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, 751 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 671, 751 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, 751 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, 751 is 1.

HCF(671, 751) = 1

HCF of 671, 751 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, 751 is 1.

Highest Common Factor of 671,751 using Euclid's algorithm

Highest Common Factor of 671,751 is 1

Step 1: Since 751 > 671, we apply the division lemma to 751 and 671, to get

751 = 671 x 1 + 80

Step 2: Since the reminder 671 ≠ 0, we apply division lemma to 80 and 671, to get

671 = 80 x 8 + 31

Step 3: We consider the new divisor 80 and the new remainder 31, and apply the division lemma to get

80 = 31 x 2 + 18

We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get

31 = 18 x 1 + 13

We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get

18 = 13 x 1 + 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 671 and 751 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(80,31) = HCF(671,80) = HCF(751,671) .

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Frequently Asked Questions on HCF of 671, 751 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, 751?

Answer: HCF of 671, 751 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 671, 751 using Euclid's Algorithm?

Answer: For arbitrary numbers 671, 751 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.