Highest Common Factor of 8142, 4657 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 8142, 4657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8142, 4657 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 8142, 4657 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 8142, 4657 is 1.

HCF(8142, 4657) = 1

HCF of 8142, 4657 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 8142, 4657 is 1.

Highest Common Factor of 8142,4657 using Euclid's algorithm

Highest Common Factor of 8142,4657 is 1

Step 1: Since 8142 > 4657, we apply the division lemma to 8142 and 4657, to get

8142 = 4657 x 1 + 3485

Step 2: Since the reminder 4657 ≠ 0, we apply division lemma to 3485 and 4657, to get

4657 = 3485 x 1 + 1172

Step 3: We consider the new divisor 3485 and the new remainder 1172, and apply the division lemma to get

3485 = 1172 x 2 + 1141

We consider the new divisor 1172 and the new remainder 1141,and apply the division lemma to get

1172 = 1141 x 1 + 31

We consider the new divisor 1141 and the new remainder 31,and apply the division lemma to get

1141 = 31 x 36 + 25

We consider the new divisor 31 and the new remainder 25,and apply the division lemma to get

31 = 25 x 1 + 6

We consider the new divisor 25 and the new remainder 6,and apply the division lemma to get

25 = 6 x 4 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8142 and 4657 is 1

Notice that 1 = HCF(6,1) = HCF(25,6) = HCF(31,25) = HCF(1141,31) = HCF(1172,1141) = HCF(3485,1172) = HCF(4657,3485) = HCF(8142,4657) .

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Frequently Asked Questions on HCF of 8142, 4657 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 8142, 4657?

Answer: HCF of 8142, 4657 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8142, 4657 using Euclid's Algorithm?

Answer: For arbitrary numbers 8142, 4657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.