Highest Common Factor of 232, 514, 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 232, 514, 634 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 232, 514, 634 is 2 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 232, 514, 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 232, 514, 634 is 2.

HCF(232, 514, 634) = 2

HCF of 232, 514, 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 232, 514, 634 is 2.

Highest Common Factor of 232,514,634 using Euclid's algorithm

Highest Common Factor of 232,514,634 is 2

Step 1: Since 514 > 232, we apply the division lemma to 514 and 232, to get

514 = 232 x 2 + 50

Step 2: Since the reminder 232 ≠ 0, we apply division lemma to 50 and 232, to get

232 = 50 x 4 + 32

Step 3: We consider the new divisor 50 and the new remainder 32, and apply the division lemma to get

50 = 32 x 1 + 18

We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get

32 = 18 x 1 + 14

We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get

18 = 14 x 1 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 232 and 514 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(50,32) = HCF(232,50) = HCF(514,232) .

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

Step 1: Since 634 > 2, we apply the division lemma to 634 and 2, to get

634 = 2 x 317 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 634 is 2

Notice that 2 = HCF(634,2) .

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Frequently Asked Questions on HCF of 232, 514, 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 232, 514, 634?

Answer: HCF of 232, 514, 634 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 232, 514, 634 using Euclid's Algorithm?

Answer: For arbitrary numbers 232, 514, 634 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.