Highest Common Factor of 635, 508, 362 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 635, 508, 362 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 635, 508, 362 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 635, 508, 362 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 635, 508, 362 is 1.

HCF(635, 508, 362) = 1

HCF of 635, 508, 362 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 635, 508, 362 is 1.

Highest Common Factor of 635,508,362 using Euclid's algorithm

Highest Common Factor of 635,508,362 is 1

Step 1: Since 635 > 508, we apply the division lemma to 635 and 508, to get

635 = 508 x 1 + 127

Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 127 and 508, to get

508 = 127 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 127, the HCF of 635 and 508 is 127

Notice that 127 = HCF(508,127) = HCF(635,508) .

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

Step 1: Since 362 > 127, we apply the division lemma to 362 and 127, to get

362 = 127 x 2 + 108

Step 2: Since the reminder 127 ≠ 0, we apply division lemma to 108 and 127, to get

127 = 108 x 1 + 19

Step 3: We consider the new divisor 108 and the new remainder 19, and apply the division lemma to get

108 = 19 x 5 + 13

We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get

19 = 13 x 1 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 127 and 362 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(108,19) = HCF(127,108) = HCF(362,127) .

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Frequently Asked Questions on HCF of 635, 508, 362 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 635, 508, 362?

Answer: HCF of 635, 508, 362 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 635, 508, 362 using Euclid's Algorithm?

Answer: For arbitrary numbers 635, 508, 362 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.