Highest Common Factor of 57, 548 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 57, 548 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 57, 548 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 57, 548 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 57, 548 is 1.

HCF(57, 548) = 1

HCF of 57, 548 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 57, 548 is 1.

Highest Common Factor of 57,548 using Euclid's algorithm

Highest Common Factor of 57,548 is 1

Step 1: Since 548 > 57, we apply the division lemma to 548 and 57, to get

548 = 57 x 9 + 35

Step 2: Since the reminder 57 ≠ 0, we apply division lemma to 35 and 57, to get

57 = 35 x 1 + 22

Step 3: We consider the new divisor 35 and the new remainder 22, and apply the division lemma to get

35 = 22 x 1 + 13

We consider the new divisor 22 and the new remainder 13,and apply the division lemma to get

22 = 13 x 1 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 57 and 548 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(35,22) = HCF(57,35) = HCF(548,57) .

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Frequently Asked Questions on HCF of 57, 548 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 57, 548?

Answer: HCF of 57, 548 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 57, 548 using Euclid's Algorithm?

Answer: For arbitrary numbers 57, 548 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.