Highest Common Factor of 861, 2159, 7398 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 861, 2159, 7398 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 861, 2159, 7398 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 861, 2159, 7398 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 861, 2159, 7398 is 1.

HCF(861, 2159, 7398) = 1

HCF of 861, 2159, 7398 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 861, 2159, 7398 is 1.

Highest Common Factor of 861,2159,7398 using Euclid's algorithm

Highest Common Factor of 861,2159,7398 is 1

Step 1: Since 2159 > 861, we apply the division lemma to 2159 and 861, to get

2159 = 861 x 2 + 437

Step 2: Since the reminder 861 ≠ 0, we apply division lemma to 437 and 861, to get

861 = 437 x 1 + 424

Step 3: We consider the new divisor 437 and the new remainder 424, and apply the division lemma to get

437 = 424 x 1 + 13

We consider the new divisor 424 and the new remainder 13,and apply the division lemma to get

424 = 13 x 32 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 861 and 2159 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(424,13) = HCF(437,424) = HCF(861,437) = HCF(2159,861) .

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

Step 1: Since 7398 > 1, we apply the division lemma to 7398 and 1, to get

7398 = 1 x 7398 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7398 is 1

Notice that 1 = HCF(7398,1) .

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Frequently Asked Questions on HCF of 861, 2159, 7398 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 861, 2159, 7398?

Answer: HCF of 861, 2159, 7398 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 861, 2159, 7398 using Euclid's Algorithm?

Answer: For arbitrary numbers 861, 2159, 7398 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.