Highest Common Factor of 691, 931, 457 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, 931, 457 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 931, 457 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, 931, 457 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, 931, 457 is 1.

HCF(691, 931, 457) = 1

HCF of 691, 931, 457 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, 931, 457 is 1.

Highest Common Factor of 691,931,457 using Euclid's algorithm

Highest Common Factor of 691,931,457 is 1

Step 1: Since 931 > 691, we apply the division lemma to 931 and 691, to get

931 = 691 x 1 + 240

Step 2: Since the reminder 691 ≠ 0, we apply division lemma to 240 and 691, to get

691 = 240 x 2 + 211

Step 3: We consider the new divisor 240 and the new remainder 211, and apply the division lemma to get

240 = 211 x 1 + 29

We consider the new divisor 211 and the new remainder 29,and apply the division lemma to get

211 = 29 x 7 + 8

We consider the new divisor 29 and the new remainder 8,and apply the division lemma to get

29 = 8 x 3 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 931 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(29,8) = HCF(211,29) = HCF(240,211) = HCF(691,240) = HCF(931,691) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 457 > 1, we apply the division lemma to 457 and 1, to get

457 = 1 x 457 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 457 is 1

Notice that 1 = HCF(457,1) .

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Frequently Asked Questions on HCF of 691, 931, 457 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, 931, 457?

Answer: HCF of 691, 931, 457 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 931, 457 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 931, 457 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.