Highest Common Factor of 691, 542 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 691, 542 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 542 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 691, 542 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 691, 542 is 1.

HCF(691, 542) = 1

HCF of 691, 542 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 691, 542 is 1.

Highest Common Factor of 691,542 using Euclid's algorithm

Highest Common Factor of 691,542 is 1

Step 1: Since 691 > 542, we apply the division lemma to 691 and 542, to get

691 = 542 x 1 + 149

Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 149 and 542, to get

542 = 149 x 3 + 95

Step 3: We consider the new divisor 149 and the new remainder 95, and apply the division lemma to get

149 = 95 x 1 + 54

We consider the new divisor 95 and the new remainder 54,and apply the division lemma to get

95 = 54 x 1 + 41

We consider the new divisor 54 and the new remainder 41,and apply the division lemma to get

54 = 41 x 1 + 13

We consider the new divisor 41 and the new remainder 13,and apply the division lemma to get

41 = 13 x 3 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 691 and 542 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(41,13) = HCF(54,41) = HCF(95,54) = HCF(149,95) = HCF(542,149) = HCF(691,542) .

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Frequently Asked Questions on HCF of 691, 542 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 691, 542?

Answer: HCF of 691, 542 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 542 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 542 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.