Highest Common Factor of 691, 980 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 691, 980 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 980 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 691, 980 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 691, 980 is 1.

HCF(691, 980) = 1

HCF of 691, 980 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 691, 980 is 1.

Highest Common Factor of 691,980 using Euclid's algorithm

Highest Common Factor of 691,980 is 1

Step 1: Since 980 > 691, we apply the division lemma to 980 and 691, to get

980 = 691 x 1 + 289

Step 2: Since the reminder 691 ≠ 0, we apply division lemma to 289 and 691, to get

691 = 289 x 2 + 113

Step 3: We consider the new divisor 289 and the new remainder 113, and apply the division lemma to get

289 = 113 x 2 + 63

We consider the new divisor 113 and the new remainder 63,and apply the division lemma to get

113 = 63 x 1 + 50

We consider the new divisor 63 and the new remainder 50,and apply the division lemma to get

63 = 50 x 1 + 13

We consider the new divisor 50 and the new remainder 13,and apply the division lemma to get

50 = 13 x 3 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 691 and 980 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(50,13) = HCF(63,50) = HCF(113,63) = HCF(289,113) = HCF(691,289) = HCF(980,691) .

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Frequently Asked Questions on HCF of 691, 980 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 691, 980?

Answer: HCF of 691, 980 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 980 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 980 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.