Highest Common Factor of 7657, 8142 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 7657, 8142 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7657, 8142 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 7657, 8142 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 7657, 8142 is 1.

HCF(7657, 8142) = 1

HCF of 7657, 8142 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 7657, 8142 is 1.

Highest Common Factor of 7657,8142 using Euclid's algorithm

Highest Common Factor of 7657,8142 is 1

Step 1: Since 8142 > 7657, we apply the division lemma to 8142 and 7657, to get

8142 = 7657 x 1 + 485

Step 2: Since the reminder 7657 ≠ 0, we apply division lemma to 485 and 7657, to get

7657 = 485 x 15 + 382

Step 3: We consider the new divisor 485 and the new remainder 382, and apply the division lemma to get

485 = 382 x 1 + 103

We consider the new divisor 382 and the new remainder 103,and apply the division lemma to get

382 = 103 x 3 + 73

We consider the new divisor 103 and the new remainder 73,and apply the division lemma to get

103 = 73 x 1 + 30

We consider the new divisor 73 and the new remainder 30,and apply the division lemma to get

73 = 30 x 2 + 13

We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get

30 = 13 x 2 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 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 7657 and 8142 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(73,30) = HCF(103,73) = HCF(382,103) = HCF(485,382) = HCF(7657,485) = HCF(8142,7657) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 7657, 8142 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 7657, 8142?

Answer: HCF of 7657, 8142 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7657, 8142 using Euclid's Algorithm?

Answer: For arbitrary numbers 7657, 8142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.