Highest Common Factor of 54, 74, 627 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 54, 74, 627 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 54, 74, 627 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 54, 74, 627 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 54, 74, 627 is 1.

HCF(54, 74, 627) = 1

HCF of 54, 74, 627 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 54, 74, 627 is 1.

Highest Common Factor of 54,74,627 using Euclid's algorithm

Highest Common Factor of 54,74,627 is 1

Step 1: Since 74 > 54, we apply the division lemma to 74 and 54, to get

74 = 54 x 1 + 20

Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 20 and 54, to get

54 = 20 x 2 + 14

Step 3: We consider the new divisor 20 and the new remainder 14, and apply the division lemma to get

20 = 14 x 1 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 54 and 74 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(54,20) = HCF(74,54) .

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

Step 1: Since 627 > 2, we apply the division lemma to 627 and 2, to get

627 = 2 x 313 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 627 is 1

Notice that 1 = HCF(2,1) = HCF(627,2) .

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Frequently Asked Questions on HCF of 54, 74, 627 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 54, 74, 627?

Answer: HCF of 54, 74, 627 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 54, 74, 627 using Euclid's Algorithm?

Answer: For arbitrary numbers 54, 74, 627 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.