Highest Common Factor of 8534, 6268 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 8534, 6268 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 8534, 6268 is 2 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 8534, 6268 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 8534, 6268 is 2.

HCF(8534, 6268) = 2

HCF of 8534, 6268 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 8534, 6268 is 2.

Highest Common Factor of 8534,6268 using Euclid's algorithm

Highest Common Factor of 8534,6268 is 2

Step 1: Since 8534 > 6268, we apply the division lemma to 8534 and 6268, to get

8534 = 6268 x 1 + 2266

Step 2: Since the reminder 6268 ≠ 0, we apply division lemma to 2266 and 6268, to get

6268 = 2266 x 2 + 1736

Step 3: We consider the new divisor 2266 and the new remainder 1736, and apply the division lemma to get

2266 = 1736 x 1 + 530

We consider the new divisor 1736 and the new remainder 530,and apply the division lemma to get

1736 = 530 x 3 + 146

We consider the new divisor 530 and the new remainder 146,and apply the division lemma to get

530 = 146 x 3 + 92

We consider the new divisor 146 and the new remainder 92,and apply the division lemma to get

146 = 92 x 1 + 54

We consider the new divisor 92 and the new remainder 54,and apply the division lemma to get

92 = 54 x 1 + 38

We consider the new divisor 54 and the new remainder 38,and apply the division lemma to get

54 = 38 x 1 + 16

We consider the new divisor 38 and the new remainder 16,and apply the division lemma to get

38 = 16 x 2 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8534 and 6268 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(38,16) = HCF(54,38) = HCF(92,54) = HCF(146,92) = HCF(530,146) = HCF(1736,530) = HCF(2266,1736) = HCF(6268,2266) = HCF(8534,6268) .

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Frequently Asked Questions on HCF of 8534, 6268 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 8534, 6268?

Answer: HCF of 8534, 6268 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8534, 6268 using Euclid's Algorithm?

Answer: For arbitrary numbers 8534, 6268 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.