Highest Common Factor of 543, 416, 77 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 543, 416, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 543, 416, 77 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 543, 416, 77 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 543, 416, 77 is 1.

HCF(543, 416, 77) = 1

HCF of 543, 416, 77 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 543, 416, 77 is 1.

Highest Common Factor of 543,416,77 using Euclid's algorithm

Highest Common Factor of 543,416,77 is 1

Step 1: Since 543 > 416, we apply the division lemma to 543 and 416, to get

543 = 416 x 1 + 127

Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 127 and 416, to get

416 = 127 x 3 + 35

Step 3: We consider the new divisor 127 and the new remainder 35, and apply the division lemma to get

127 = 35 x 3 + 22

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 543 and 416 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(35,22) = HCF(127,35) = HCF(416,127) = HCF(543,416) .

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

Step 1: Since 77 > 1, we apply the division lemma to 77 and 1, to get

77 = 1 x 77 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77 is 1

Notice that 1 = HCF(77,1) .

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Frequently Asked Questions on HCF of 543, 416, 77 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 543, 416, 77?

Answer: HCF of 543, 416, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 543, 416, 77 using Euclid's Algorithm?

Answer: For arbitrary numbers 543, 416, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.