Highest Common Factor of 637, 854, 362, 724 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, 854, 362, 724 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 637, 854, 362, 724 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, 854, 362, 724 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, 854, 362, 724 is 1.

HCF(637, 854, 362, 724) = 1

HCF of 637, 854, 362, 724 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, 854, 362, 724 is 1.

Highest Common Factor of 637,854,362,724 using Euclid's algorithm

Highest Common Factor of 637,854,362,724 is 1

Step 1: Since 854 > 637, we apply the division lemma to 854 and 637, to get

854 = 637 x 1 + 217

Step 2: Since the reminder 637 ≠ 0, we apply division lemma to 217 and 637, to get

637 = 217 x 2 + 203

Step 3: We consider the new divisor 217 and the new remainder 203, and apply the division lemma to get

217 = 203 x 1 + 14

We consider the new divisor 203 and the new remainder 14,and apply the division lemma to get

203 = 14 x 14 + 7

We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get

14 = 7 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 637 and 854 is 7

Notice that 7 = HCF(14,7) = HCF(203,14) = HCF(217,203) = HCF(637,217) = HCF(854,637) .

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

Step 1: Since 362 > 7, we apply the division lemma to 362 and 7, to get

362 = 7 x 51 + 5

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 5 and 7, to get

7 = 5 x 1 + 2

Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get

5 = 2 x 2 + 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 7 and 362 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(362,7) .

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

Step 1: Since 724 > 1, we apply the division lemma to 724 and 1, to get

724 = 1 x 724 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 724 is 1

Notice that 1 = HCF(724,1) .

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Frequently Asked Questions on HCF of 637, 854, 362, 724 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, 854, 362, 724?

Answer: HCF of 637, 854, 362, 724 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 637, 854, 362, 724 using Euclid's Algorithm?

Answer: For arbitrary numbers 637, 854, 362, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.