Highest Common Factor of 3720, 9718 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 3720, 9718 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 3720, 9718 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 3720, 9718 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 3720, 9718 is 2.

HCF(3720, 9718) = 2

HCF of 3720, 9718 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 3720, 9718 is 2.

Highest Common Factor of 3720,9718 using Euclid's algorithm

Highest Common Factor of 3720,9718 is 2

Step 1: Since 9718 > 3720, we apply the division lemma to 9718 and 3720, to get

9718 = 3720 x 2 + 2278

Step 2: Since the reminder 3720 ≠ 0, we apply division lemma to 2278 and 3720, to get

3720 = 2278 x 1 + 1442

Step 3: We consider the new divisor 2278 and the new remainder 1442, and apply the division lemma to get

2278 = 1442 x 1 + 836

We consider the new divisor 1442 and the new remainder 836,and apply the division lemma to get

1442 = 836 x 1 + 606

We consider the new divisor 836 and the new remainder 606,and apply the division lemma to get

836 = 606 x 1 + 230

We consider the new divisor 606 and the new remainder 230,and apply the division lemma to get

606 = 230 x 2 + 146

We consider the new divisor 230 and the new remainder 146,and apply the division lemma to get

230 = 146 x 1 + 84

We consider the new divisor 146 and the new remainder 84,and apply the division lemma to get

146 = 84 x 1 + 62

We consider the new divisor 84 and the new remainder 62,and apply the division lemma to get

84 = 62 x 1 + 22

We consider the new divisor 62 and the new remainder 22,and apply the division lemma to get

62 = 22 x 2 + 18

We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get

22 = 18 x 1 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 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 3720 and 9718 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(62,22) = HCF(84,62) = HCF(146,84) = HCF(230,146) = HCF(606,230) = HCF(836,606) = HCF(1442,836) = HCF(2278,1442) = HCF(3720,2278) = HCF(9718,3720) .

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Frequently Asked Questions on HCF of 3720, 9718 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 3720, 9718?

Answer: HCF of 3720, 9718 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3720, 9718 using Euclid's Algorithm?

Answer: For arbitrary numbers 3720, 9718 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.