Highest Common Factor of 8421, 9299, 26612 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 8421, 9299, 26612 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8421, 9299, 26612 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 8421, 9299, 26612 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 8421, 9299, 26612 is 1.

HCF(8421, 9299, 26612) = 1

HCF of 8421, 9299, 26612 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 8421, 9299, 26612 is 1.

Highest Common Factor of 8421,9299,26612 using Euclid's algorithm

Highest Common Factor of 8421,9299,26612 is 1

Step 1: Since 9299 > 8421, we apply the division lemma to 9299 and 8421, to get

9299 = 8421 x 1 + 878

Step 2: Since the reminder 8421 ≠ 0, we apply division lemma to 878 and 8421, to get

8421 = 878 x 9 + 519

Step 3: We consider the new divisor 878 and the new remainder 519, and apply the division lemma to get

878 = 519 x 1 + 359

We consider the new divisor 519 and the new remainder 359,and apply the division lemma to get

519 = 359 x 1 + 160

We consider the new divisor 359 and the new remainder 160,and apply the division lemma to get

359 = 160 x 2 + 39

We consider the new divisor 160 and the new remainder 39,and apply the division lemma to get

160 = 39 x 4 + 4

We consider the new divisor 39 and the new remainder 4,and apply the division lemma to get

39 = 4 x 9 + 3

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

4 = 3 x 1 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8421 and 9299 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(39,4) = HCF(160,39) = HCF(359,160) = HCF(519,359) = HCF(878,519) = HCF(8421,878) = HCF(9299,8421) .

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

Step 1: Since 26612 > 1, we apply the division lemma to 26612 and 1, to get

26612 = 1 x 26612 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 26612 is 1

Notice that 1 = HCF(26612,1) .

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Frequently Asked Questions on HCF of 8421, 9299, 26612 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 8421, 9299, 26612?

Answer: HCF of 8421, 9299, 26612 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8421, 9299, 26612 using Euclid's Algorithm?

Answer: For arbitrary numbers 8421, 9299, 26612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.