Highest Common Factor of 541, 691, 51 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 541, 691, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 541, 691, 51 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 541, 691, 51 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 541, 691, 51 is 1.

HCF(541, 691, 51) = 1

HCF of 541, 691, 51 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 541, 691, 51 is 1.

Highest Common Factor of 541,691,51 using Euclid's algorithm

Highest Common Factor of 541,691,51 is 1

Step 1: Since 691 > 541, we apply the division lemma to 691 and 541, to get

691 = 541 x 1 + 150

Step 2: Since the reminder 541 ≠ 0, we apply division lemma to 150 and 541, to get

541 = 150 x 3 + 91

Step 3: We consider the new divisor 150 and the new remainder 91, and apply the division lemma to get

150 = 91 x 1 + 59

We consider the new divisor 91 and the new remainder 59,and apply the division lemma to get

91 = 59 x 1 + 32

We consider the new divisor 59 and the new remainder 32,and apply the division lemma to get

59 = 32 x 1 + 27

We consider the new divisor 32 and the new remainder 27,and apply the division lemma to get

32 = 27 x 1 + 5

We consider the new divisor 27 and the new remainder 5,and apply the division lemma to get

27 = 5 x 5 + 2

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 541 and 691 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(27,5) = HCF(32,27) = HCF(59,32) = HCF(91,59) = HCF(150,91) = HCF(541,150) = HCF(691,541) .

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

Step 1: Since 51 > 1, we apply the division lemma to 51 and 1, to get

51 = 1 x 51 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51 is 1

Notice that 1 = HCF(51,1) .

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Frequently Asked Questions on HCF of 541, 691, 51 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 541, 691, 51?

Answer: HCF of 541, 691, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 541, 691, 51 using Euclid's Algorithm?

Answer: For arbitrary numbers 541, 691, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.