Highest Common Factor of 2135, 9278 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 2135, 9278 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2135, 9278 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 2135, 9278 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 2135, 9278 is 1.

HCF(2135, 9278) = 1

HCF of 2135, 9278 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 2135, 9278 is 1.

Highest Common Factor of 2135,9278 using Euclid's algorithm

Highest Common Factor of 2135,9278 is 1

Step 1: Since 9278 > 2135, we apply the division lemma to 9278 and 2135, to get

9278 = 2135 x 4 + 738

Step 2: Since the reminder 2135 ≠ 0, we apply division lemma to 738 and 2135, to get

2135 = 738 x 2 + 659

Step 3: We consider the new divisor 738 and the new remainder 659, and apply the division lemma to get

738 = 659 x 1 + 79

We consider the new divisor 659 and the new remainder 79,and apply the division lemma to get

659 = 79 x 8 + 27

We consider the new divisor 79 and the new remainder 27,and apply the division lemma to get

79 = 27 x 2 + 25

We consider the new divisor 27 and the new remainder 25,and apply the division lemma to get

27 = 25 x 1 + 2

We consider the new divisor 25 and the new remainder 2,and apply the division lemma to get

25 = 2 x 12 + 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 2135 and 9278 is 1

Notice that 1 = HCF(2,1) = HCF(25,2) = HCF(27,25) = HCF(79,27) = HCF(659,79) = HCF(738,659) = HCF(2135,738) = HCF(9278,2135) .

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Frequently Asked Questions on HCF of 2135, 9278 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 2135, 9278?

Answer: HCF of 2135, 9278 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2135, 9278 using Euclid's Algorithm?

Answer: For arbitrary numbers 2135, 9278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.