Highest Common Factor of 2931, 8024, 53754 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 2931, 8024, 53754 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2931, 8024, 53754 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 2931, 8024, 53754 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 2931, 8024, 53754 is 1.

HCF(2931, 8024, 53754) = 1

HCF of 2931, 8024, 53754 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 2931, 8024, 53754 is 1.

Highest Common Factor of 2931,8024,53754 using Euclid's algorithm

Highest Common Factor of 2931,8024,53754 is 1

Step 1: Since 8024 > 2931, we apply the division lemma to 8024 and 2931, to get

8024 = 2931 x 2 + 2162

Step 2: Since the reminder 2931 ≠ 0, we apply division lemma to 2162 and 2931, to get

2931 = 2162 x 1 + 769

Step 3: We consider the new divisor 2162 and the new remainder 769, and apply the division lemma to get

2162 = 769 x 2 + 624

We consider the new divisor 769 and the new remainder 624,and apply the division lemma to get

769 = 624 x 1 + 145

We consider the new divisor 624 and the new remainder 145,and apply the division lemma to get

624 = 145 x 4 + 44

We consider the new divisor 145 and the new remainder 44,and apply the division lemma to get

145 = 44 x 3 + 13

We consider the new divisor 44 and the new remainder 13,and apply the division lemma to get

44 = 13 x 3 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 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 2931 and 8024 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(44,13) = HCF(145,44) = HCF(624,145) = HCF(769,624) = HCF(2162,769) = HCF(2931,2162) = HCF(8024,2931) .

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

Step 1: Since 53754 > 1, we apply the division lemma to 53754 and 1, to get

53754 = 1 x 53754 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 53754 is 1

Notice that 1 = HCF(53754,1) .

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Frequently Asked Questions on HCF of 2931, 8024, 53754 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 2931, 8024, 53754?

Answer: HCF of 2931, 8024, 53754 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2931, 8024, 53754 using Euclid's Algorithm?

Answer: For arbitrary numbers 2931, 8024, 53754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.