Highest Common Factor of 637, 2151, 2096 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 637, 2151, 2096 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 637, 2151, 2096 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 637, 2151, 2096 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 637, 2151, 2096 is 1.

HCF(637, 2151, 2096) = 1

HCF of 637, 2151, 2096 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 637, 2151, 2096 is 1.

Highest Common Factor of 637,2151,2096 using Euclid's algorithm

Highest Common Factor of 637,2151,2096 is 1

Step 1: Since 2151 > 637, we apply the division lemma to 2151 and 637, to get

2151 = 637 x 3 + 240

Step 2: Since the reminder 637 ≠ 0, we apply division lemma to 240 and 637, to get

637 = 240 x 2 + 157

Step 3: We consider the new divisor 240 and the new remainder 157, and apply the division lemma to get

240 = 157 x 1 + 83

We consider the new divisor 157 and the new remainder 83,and apply the division lemma to get

157 = 83 x 1 + 74

We consider the new divisor 83 and the new remainder 74,and apply the division lemma to get

83 = 74 x 1 + 9

We consider the new divisor 74 and the new remainder 9,and apply the division lemma to get

74 = 9 x 8 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 637 and 2151 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(74,9) = HCF(83,74) = HCF(157,83) = HCF(240,157) = HCF(637,240) = HCF(2151,637) .

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

Step 1: Since 2096 > 1, we apply the division lemma to 2096 and 1, to get

2096 = 1 x 2096 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2096 is 1

Notice that 1 = HCF(2096,1) .

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Frequently Asked Questions on HCF of 637, 2151, 2096 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 637, 2151, 2096?

Answer: HCF of 637, 2151, 2096 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 637, 2151, 2096 using Euclid's Algorithm?

Answer: For arbitrary numbers 637, 2151, 2096 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.