Highest Common Factor of 491, 696, 51 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 491, 696, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 491, 696, 51 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 491, 696, 51 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 491, 696, 51 is 1.

HCF(491, 696, 51) = 1

HCF of 491, 696, 51 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 491, 696, 51 is 1.

Highest Common Factor of 491,696,51 using Euclid's algorithm

Highest Common Factor of 491,696,51 is 1

Step 1: Since 696 > 491, we apply the division lemma to 696 and 491, to get

696 = 491 x 1 + 205

Step 2: Since the reminder 491 ≠ 0, we apply division lemma to 205 and 491, to get

491 = 205 x 2 + 81

Step 3: We consider the new divisor 205 and the new remainder 81, and apply the division lemma to get

205 = 81 x 2 + 43

We consider the new divisor 81 and the new remainder 43,and apply the division lemma to get

81 = 43 x 1 + 38

We consider the new divisor 43 and the new remainder 38,and apply the division lemma to get

43 = 38 x 1 + 5

We consider the new divisor 38 and the new remainder 5,and apply the division lemma to get

38 = 5 x 7 + 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 491 and 696 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(38,5) = HCF(43,38) = HCF(81,43) = HCF(205,81) = HCF(491,205) = HCF(696,491) .

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

Step 1: Since 51 > 1, we apply the division lemma to 51 and 1, to get

51 = 1 x 51 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51 is 1

Notice that 1 = HCF(51,1) .

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Frequently Asked Questions on HCF of 491, 696, 51 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 491, 696, 51?

Answer: HCF of 491, 696, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 491, 696, 51 using Euclid's Algorithm?

Answer: For arbitrary numbers 491, 696, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.