Highest Common Factor of 687, 291, 464 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 687, 291, 464 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 687, 291, 464 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 687, 291, 464 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 687, 291, 464 is 1.

HCF(687, 291, 464) = 1

HCF of 687, 291, 464 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 687, 291, 464 is 1.

Highest Common Factor of 687,291,464 using Euclid's algorithm

Highest Common Factor of 687,291,464 is 1

Step 1: Since 687 > 291, we apply the division lemma to 687 and 291, to get

687 = 291 x 2 + 105

Step 2: Since the reminder 291 ≠ 0, we apply division lemma to 105 and 291, to get

291 = 105 x 2 + 81

Step 3: We consider the new divisor 105 and the new remainder 81, and apply the division lemma to get

105 = 81 x 1 + 24

We consider the new divisor 81 and the new remainder 24,and apply the division lemma to get

81 = 24 x 3 + 9

We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get

24 = 9 x 2 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 687 and 291 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(81,24) = HCF(105,81) = HCF(291,105) = HCF(687,291) .

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

Step 1: Since 464 > 3, we apply the division lemma to 464 and 3, to get

464 = 3 x 154 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 464 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(464,3) .

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Frequently Asked Questions on HCF of 687, 291, 464 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 687, 291, 464?

Answer: HCF of 687, 291, 464 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 687, 291, 464 using Euclid's Algorithm?

Answer: For arbitrary numbers 687, 291, 464 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.