Highest Common Factor of 981, 691 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 981, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 981, 691 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 981, 691 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 981, 691 is 1.

HCF(981, 691) = 1

HCF of 981, 691 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 981, 691 is 1.

Highest Common Factor of 981,691 using Euclid's algorithm

Highest Common Factor of 981,691 is 1

Step 1: Since 981 > 691, we apply the division lemma to 981 and 691, to get

981 = 691 x 1 + 290

Step 2: Since the reminder 691 ≠ 0, we apply division lemma to 290 and 691, to get

691 = 290 x 2 + 111

Step 3: We consider the new divisor 290 and the new remainder 111, and apply the division lemma to get

290 = 111 x 2 + 68

We consider the new divisor 111 and the new remainder 68,and apply the division lemma to get

111 = 68 x 1 + 43

We consider the new divisor 68 and the new remainder 43,and apply the division lemma to get

68 = 43 x 1 + 25

We consider the new divisor 43 and the new remainder 25,and apply the division lemma to get

43 = 25 x 1 + 18

We consider the new divisor 25 and the new remainder 18,and apply the division lemma to get

25 = 18 x 1 + 7

We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get

18 = 7 x 2 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 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 981 and 691 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(25,18) = HCF(43,25) = HCF(68,43) = HCF(111,68) = HCF(290,111) = HCF(691,290) = HCF(981,691) .

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Frequently Asked Questions on HCF of 981, 691 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 981, 691?

Answer: HCF of 981, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 981, 691 using Euclid's Algorithm?

Answer: For arbitrary numbers 981, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.