Highest Common Factor of 9678, 2635, 27529 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 9678, 2635, 27529 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9678, 2635, 27529 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 9678, 2635, 27529 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 9678, 2635, 27529 is 1.

HCF(9678, 2635, 27529) = 1

HCF of 9678, 2635, 27529 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 9678, 2635, 27529 is 1.

Highest Common Factor of 9678,2635,27529 using Euclid's algorithm

Highest Common Factor of 9678,2635,27529 is 1

Step 1: Since 9678 > 2635, we apply the division lemma to 9678 and 2635, to get

9678 = 2635 x 3 + 1773

Step 2: Since the reminder 2635 ≠ 0, we apply division lemma to 1773 and 2635, to get

2635 = 1773 x 1 + 862

Step 3: We consider the new divisor 1773 and the new remainder 862, and apply the division lemma to get

1773 = 862 x 2 + 49

We consider the new divisor 862 and the new remainder 49,and apply the division lemma to get

862 = 49 x 17 + 29

We consider the new divisor 49 and the new remainder 29,and apply the division lemma to get

49 = 29 x 1 + 20

We consider the new divisor 29 and the new remainder 20,and apply the division lemma to get

29 = 20 x 1 + 9

We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get

20 = 9 x 2 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 9678 and 2635 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(29,20) = HCF(49,29) = HCF(862,49) = HCF(1773,862) = HCF(2635,1773) = HCF(9678,2635) .

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

Step 1: Since 27529 > 1, we apply the division lemma to 27529 and 1, to get

27529 = 1 x 27529 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 27529 is 1

Notice that 1 = HCF(27529,1) .

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Frequently Asked Questions on HCF of 9678, 2635, 27529 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 9678, 2635, 27529?

Answer: HCF of 9678, 2635, 27529 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9678, 2635, 27529 using Euclid's Algorithm?

Answer: For arbitrary numbers 9678, 2635, 27529 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.