Highest Common Factor of 237, 810, 634 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 237, 810, 634 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 237, 810, 634 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 237, 810, 634 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 237, 810, 634 is 1.

HCF(237, 810, 634) = 1

HCF of 237, 810, 634 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 237, 810, 634 is 1.

Highest Common Factor of 237,810,634 using Euclid's algorithm

Highest Common Factor of 237,810,634 is 1

Step 1: Since 810 > 237, we apply the division lemma to 810 and 237, to get

810 = 237 x 3 + 99

Step 2: Since the reminder 237 ≠ 0, we apply division lemma to 99 and 237, to get

237 = 99 x 2 + 39

Step 3: We consider the new divisor 99 and the new remainder 39, and apply the division lemma to get

99 = 39 x 2 + 21

We consider the new divisor 39 and the new remainder 21,and apply the division lemma to get

39 = 21 x 1 + 18

We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get

21 = 18 x 1 + 3

We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get

18 = 3 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 237 and 810 is 3

Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(39,21) = HCF(99,39) = HCF(237,99) = HCF(810,237) .

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

Step 1: Since 634 > 3, we apply the division lemma to 634 and 3, to get

634 = 3 x 211 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 634 is 1

Notice that 1 = HCF(3,1) = HCF(634,3) .

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Frequently Asked Questions on HCF of 237, 810, 634 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 237, 810, 634?

Answer: HCF of 237, 810, 634 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 237, 810, 634 using Euclid's Algorithm?

Answer: For arbitrary numbers 237, 810, 634 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.