Highest Common Factor of 960, 9115, 2694 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 960, 9115, 2694 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 960, 9115, 2694 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 960, 9115, 2694 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 960, 9115, 2694 is 1.

HCF(960, 9115, 2694) = 1

HCF of 960, 9115, 2694 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 960, 9115, 2694 is 1.

Highest Common Factor of 960,9115,2694 using Euclid's algorithm

Highest Common Factor of 960,9115,2694 is 1

Step 1: Since 9115 > 960, we apply the division lemma to 9115 and 960, to get

9115 = 960 x 9 + 475

Step 2: Since the reminder 960 ≠ 0, we apply division lemma to 475 and 960, to get

960 = 475 x 2 + 10

Step 3: We consider the new divisor 475 and the new remainder 10, and apply the division lemma to get

475 = 10 x 47 + 5

We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 960 and 9115 is 5

Notice that 5 = HCF(10,5) = HCF(475,10) = HCF(960,475) = HCF(9115,960) .

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

Step 1: Since 2694 > 5, we apply the division lemma to 2694 and 5, to get

2694 = 5 x 538 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 2694 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(2694,5) .

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Frequently Asked Questions on HCF of 960, 9115, 2694 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 960, 9115, 2694?

Answer: HCF of 960, 9115, 2694 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 960, 9115, 2694 using Euclid's Algorithm?

Answer: For arbitrary numbers 960, 9115, 2694 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.