Highest Common Factor of 8590, 4637, 21701 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 8590, 4637, 21701 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8590, 4637, 21701 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 8590, 4637, 21701 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 8590, 4637, 21701 is 1.

HCF(8590, 4637, 21701) = 1

HCF of 8590, 4637, 21701 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 8590, 4637, 21701 is 1.

Highest Common Factor of 8590,4637,21701 using Euclid's algorithm

Highest Common Factor of 8590,4637,21701 is 1

Step 1: Since 8590 > 4637, we apply the division lemma to 8590 and 4637, to get

8590 = 4637 x 1 + 3953

Step 2: Since the reminder 4637 ≠ 0, we apply division lemma to 3953 and 4637, to get

4637 = 3953 x 1 + 684

Step 3: We consider the new divisor 3953 and the new remainder 684, and apply the division lemma to get

3953 = 684 x 5 + 533

We consider the new divisor 684 and the new remainder 533,and apply the division lemma to get

684 = 533 x 1 + 151

We consider the new divisor 533 and the new remainder 151,and apply the division lemma to get

533 = 151 x 3 + 80

We consider the new divisor 151 and the new remainder 80,and apply the division lemma to get

151 = 80 x 1 + 71

We consider the new divisor 80 and the new remainder 71,and apply the division lemma to get

80 = 71 x 1 + 9

We consider the new divisor 71 and the new remainder 9,and apply the division lemma to get

71 = 9 x 7 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8590 and 4637 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(71,9) = HCF(80,71) = HCF(151,80) = HCF(533,151) = HCF(684,533) = HCF(3953,684) = HCF(4637,3953) = HCF(8590,4637) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 21701 > 1, we apply the division lemma to 21701 and 1, to get

21701 = 1 x 21701 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21701 is 1

Notice that 1 = HCF(21701,1) .

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Frequently Asked Questions on HCF of 8590, 4637, 21701 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 8590, 4637, 21701?

Answer: HCF of 8590, 4637, 21701 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8590, 4637, 21701 using Euclid's Algorithm?

Answer: For arbitrary numbers 8590, 4637, 21701 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.