Highest Common Factor of 637, 338, 62 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, 338, 62 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 637, 338, 62 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, 338, 62 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, 338, 62 is 1.

HCF(637, 338, 62) = 1

HCF of 637, 338, 62 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, 338, 62 is 1.

Highest Common Factor of 637,338,62 using Euclid's algorithm

Highest Common Factor of 637,338,62 is 1

Step 1: Since 637 > 338, we apply the division lemma to 637 and 338, to get

637 = 338 x 1 + 299

Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 299 and 338, to get

338 = 299 x 1 + 39

Step 3: We consider the new divisor 299 and the new remainder 39, and apply the division lemma to get

299 = 39 x 7 + 26

We consider the new divisor 39 and the new remainder 26,and apply the division lemma to get

39 = 26 x 1 + 13

We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 637 and 338 is 13

Notice that 13 = HCF(26,13) = HCF(39,26) = HCF(299,39) = HCF(338,299) = HCF(637,338) .

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

Step 1: Since 62 > 13, we apply the division lemma to 62 and 13, to get

62 = 13 x 4 + 10

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 10 and 13, to get

13 = 10 x 1 + 3

Step 3: We consider the new divisor 10 and the new remainder 3, and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma 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 13 and 62 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(62,13) .

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Frequently Asked Questions on HCF of 637, 338, 62 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, 338, 62?

Answer: HCF of 637, 338, 62 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 637, 338, 62 using Euclid's Algorithm?

Answer: For arbitrary numbers 637, 338, 62 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.