Highest Common Factor of 864, 614, 261 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 864, 614, 261 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 864, 614, 261 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 864, 614, 261 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 864, 614, 261 is 1.

HCF(864, 614, 261) = 1

HCF of 864, 614, 261 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 864, 614, 261 is 1.

Highest Common Factor of 864,614,261 using Euclid's algorithm

Highest Common Factor of 864,614,261 is 1

Step 1: Since 864 > 614, we apply the division lemma to 864 and 614, to get

864 = 614 x 1 + 250

Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 250 and 614, to get

614 = 250 x 2 + 114

Step 3: We consider the new divisor 250 and the new remainder 114, and apply the division lemma to get

250 = 114 x 2 + 22

We consider the new divisor 114 and the new remainder 22,and apply the division lemma to get

114 = 22 x 5 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 864 and 614 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(114,22) = HCF(250,114) = HCF(614,250) = HCF(864,614) .

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

Step 1: Since 261 > 2, we apply the division lemma to 261 and 2, to get

261 = 2 x 130 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 261 is 1

Notice that 1 = HCF(2,1) = HCF(261,2) .

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Frequently Asked Questions on HCF of 864, 614, 261 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 864, 614, 261?

Answer: HCF of 864, 614, 261 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 864, 614, 261 using Euclid's Algorithm?

Answer: For arbitrary numbers 864, 614, 261 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.