Highest Common Factor of 680, 9937 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 680, 9937 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 680, 9937 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 680, 9937 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 680, 9937 is 1.

HCF(680, 9937) = 1

HCF of 680, 9937 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 680, 9937 is 1.

Highest Common Factor of 680,9937 using Euclid's algorithm

Highest Common Factor of 680,9937 is 1

Step 1: Since 9937 > 680, we apply the division lemma to 9937 and 680, to get

9937 = 680 x 14 + 417

Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 417 and 680, to get

680 = 417 x 1 + 263

Step 3: We consider the new divisor 417 and the new remainder 263, and apply the division lemma to get

417 = 263 x 1 + 154

We consider the new divisor 263 and the new remainder 154,and apply the division lemma to get

263 = 154 x 1 + 109

We consider the new divisor 154 and the new remainder 109,and apply the division lemma to get

154 = 109 x 1 + 45

We consider the new divisor 109 and the new remainder 45,and apply the division lemma to get

109 = 45 x 2 + 19

We consider the new divisor 45 and the new remainder 19,and apply the division lemma to get

45 = 19 x 2 + 7

We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get

19 = 7 x 2 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 680 and 9937 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(45,19) = HCF(109,45) = HCF(154,109) = HCF(263,154) = HCF(417,263) = HCF(680,417) = HCF(9937,680) .

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Frequently Asked Questions on HCF of 680, 9937 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 680, 9937?

Answer: HCF of 680, 9937 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 680, 9937 using Euclid's Algorithm?

Answer: For arbitrary numbers 680, 9937 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.