Highest Common Factor of 457, 7891, 6134 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 457, 7891, 6134 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 457, 7891, 6134 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 457, 7891, 6134 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 457, 7891, 6134 is 1.

HCF(457, 7891, 6134) = 1

HCF of 457, 7891, 6134 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 457, 7891, 6134 is 1.

Highest Common Factor of 457,7891,6134 using Euclid's algorithm

Highest Common Factor of 457,7891,6134 is 1

Step 1: Since 7891 > 457, we apply the division lemma to 7891 and 457, to get

7891 = 457 x 17 + 122

Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 122 and 457, to get

457 = 122 x 3 + 91

Step 3: We consider the new divisor 122 and the new remainder 91, and apply the division lemma to get

122 = 91 x 1 + 31

We consider the new divisor 91 and the new remainder 31,and apply the division lemma to get

91 = 31 x 2 + 29

We consider the new divisor 31 and the new remainder 29,and apply the division lemma to get

31 = 29 x 1 + 2

We consider the new divisor 29 and the new remainder 2,and apply the division lemma to get

29 = 2 x 14 + 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 457 and 7891 is 1

Notice that 1 = HCF(2,1) = HCF(29,2) = HCF(31,29) = HCF(91,31) = HCF(122,91) = HCF(457,122) = HCF(7891,457) .

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

Step 1: Since 6134 > 1, we apply the division lemma to 6134 and 1, to get

6134 = 1 x 6134 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6134 is 1

Notice that 1 = HCF(6134,1) .

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Frequently Asked Questions on HCF of 457, 7891, 6134 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 457, 7891, 6134?

Answer: HCF of 457, 7891, 6134 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 457, 7891, 6134 using Euclid's Algorithm?

Answer: For arbitrary numbers 457, 7891, 6134 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.