Highest Common Factor of 3872, 6967 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 3872, 6967 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3872, 6967 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 3872, 6967 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 3872, 6967 is 1.

HCF(3872, 6967) = 1

HCF of 3872, 6967 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 3872, 6967 is 1.

Highest Common Factor of 3872,6967 using Euclid's algorithm

Highest Common Factor of 3872,6967 is 1

Step 1: Since 6967 > 3872, we apply the division lemma to 6967 and 3872, to get

6967 = 3872 x 1 + 3095

Step 2: Since the reminder 3872 ≠ 0, we apply division lemma to 3095 and 3872, to get

3872 = 3095 x 1 + 777

Step 3: We consider the new divisor 3095 and the new remainder 777, and apply the division lemma to get

3095 = 777 x 3 + 764

We consider the new divisor 777 and the new remainder 764,and apply the division lemma to get

777 = 764 x 1 + 13

We consider the new divisor 764 and the new remainder 13,and apply the division lemma to get

764 = 13 x 58 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3872 and 6967 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(764,13) = HCF(777,764) = HCF(3095,777) = HCF(3872,3095) = HCF(6967,3872) .

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Frequently Asked Questions on HCF of 3872, 6967 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 3872, 6967?

Answer: HCF of 3872, 6967 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3872, 6967 using Euclid's Algorithm?

Answer: For arbitrary numbers 3872, 6967 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.