Highest Common Factor of 635, 974 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, 974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 635, 974 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, 974 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, 974 is 1.

HCF(635, 974) = 1

HCF of 635, 974 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, 974 is 1.

Highest Common Factor of 635,974 using Euclid's algorithm

Highest Common Factor of 635,974 is 1

Step 1: Since 974 > 635, we apply the division lemma to 974 and 635, to get

974 = 635 x 1 + 339

Step 2: Since the reminder 635 ≠ 0, we apply division lemma to 339 and 635, to get

635 = 339 x 1 + 296

Step 3: We consider the new divisor 339 and the new remainder 296, and apply the division lemma to get

339 = 296 x 1 + 43

We consider the new divisor 296 and the new remainder 43,and apply the division lemma to get

296 = 43 x 6 + 38

We consider the new divisor 43 and the new remainder 38,and apply the division lemma to get

43 = 38 x 1 + 5

We consider the new divisor 38 and the new remainder 5,and apply the division lemma to get

38 = 5 x 7 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 635 and 974 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(38,5) = HCF(43,38) = HCF(296,43) = HCF(339,296) = HCF(635,339) = HCF(974,635) .

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Frequently Asked Questions on HCF of 635, 974 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, 974?

Answer: HCF of 635, 974 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 635, 974 using Euclid's Algorithm?

Answer: For arbitrary numbers 635, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.