Highest Common Factor of 3140, 8268 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 3140, 8268 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 3140, 8268 is 4 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 3140, 8268 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 3140, 8268 is 4.

HCF(3140, 8268) = 4

HCF of 3140, 8268 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 3140, 8268 is 4.

Highest Common Factor of 3140,8268 using Euclid's algorithm

Highest Common Factor of 3140,8268 is 4

Step 1: Since 8268 > 3140, we apply the division lemma to 8268 and 3140, to get

8268 = 3140 x 2 + 1988

Step 2: Since the reminder 3140 ≠ 0, we apply division lemma to 1988 and 3140, to get

3140 = 1988 x 1 + 1152

Step 3: We consider the new divisor 1988 and the new remainder 1152, and apply the division lemma to get

1988 = 1152 x 1 + 836

We consider the new divisor 1152 and the new remainder 836,and apply the division lemma to get

1152 = 836 x 1 + 316

We consider the new divisor 836 and the new remainder 316,and apply the division lemma to get

836 = 316 x 2 + 204

We consider the new divisor 316 and the new remainder 204,and apply the division lemma to get

316 = 204 x 1 + 112

We consider the new divisor 204 and the new remainder 112,and apply the division lemma to get

204 = 112 x 1 + 92

We consider the new divisor 112 and the new remainder 92,and apply the division lemma to get

112 = 92 x 1 + 20

We consider the new divisor 92 and the new remainder 20,and apply the division lemma to get

92 = 20 x 4 + 12

We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get

20 = 12 x 1 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 3140 and 8268 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(92,20) = HCF(112,92) = HCF(204,112) = HCF(316,204) = HCF(836,316) = HCF(1152,836) = HCF(1988,1152) = HCF(3140,1988) = HCF(8268,3140) .

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Frequently Asked Questions on HCF of 3140, 8268 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 3140, 8268?

Answer: HCF of 3140, 8268 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3140, 8268 using Euclid's Algorithm?

Answer: For arbitrary numbers 3140, 8268 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.