Highest Common Factor of 7137, 5218 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 7137, 5218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7137, 5218 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 7137, 5218 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 7137, 5218 is 1.

HCF(7137, 5218) = 1

HCF of 7137, 5218 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 7137, 5218 is 1.

Highest Common Factor of 7137,5218 using Euclid's algorithm

Highest Common Factor of 7137,5218 is 1

Step 1: Since 7137 > 5218, we apply the division lemma to 7137 and 5218, to get

7137 = 5218 x 1 + 1919

Step 2: Since the reminder 5218 ≠ 0, we apply division lemma to 1919 and 5218, to get

5218 = 1919 x 2 + 1380

Step 3: We consider the new divisor 1919 and the new remainder 1380, and apply the division lemma to get

1919 = 1380 x 1 + 539

We consider the new divisor 1380 and the new remainder 539,and apply the division lemma to get

1380 = 539 x 2 + 302

We consider the new divisor 539 and the new remainder 302,and apply the division lemma to get

539 = 302 x 1 + 237

We consider the new divisor 302 and the new remainder 237,and apply the division lemma to get

302 = 237 x 1 + 65

We consider the new divisor 237 and the new remainder 65,and apply the division lemma to get

237 = 65 x 3 + 42

We consider the new divisor 65 and the new remainder 42,and apply the division lemma to get

65 = 42 x 1 + 23

We consider the new divisor 42 and the new remainder 23,and apply the division lemma to get

42 = 23 x 1 + 19

We consider the new divisor 23 and the new remainder 19,and apply the division lemma to get

23 = 19 x 1 + 4

We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get

19 = 4 x 4 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7137 and 5218 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(23,19) = HCF(42,23) = HCF(65,42) = HCF(237,65) = HCF(302,237) = HCF(539,302) = HCF(1380,539) = HCF(1919,1380) = HCF(5218,1919) = HCF(7137,5218) .

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Frequently Asked Questions on HCF of 7137, 5218 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 7137, 5218?

Answer: HCF of 7137, 5218 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7137, 5218 using Euclid's Algorithm?

Answer: For arbitrary numbers 7137, 5218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.