Highest Common Factor of 8537, 6622, 17146 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 8537, 6622, 17146 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8537, 6622, 17146 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 8537, 6622, 17146 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 8537, 6622, 17146 is 1.

HCF(8537, 6622, 17146) = 1

HCF of 8537, 6622, 17146 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 8537, 6622, 17146 is 1.

Highest Common Factor of 8537,6622,17146 using Euclid's algorithm

Highest Common Factor of 8537,6622,17146 is 1

Step 1: Since 8537 > 6622, we apply the division lemma to 8537 and 6622, to get

8537 = 6622 x 1 + 1915

Step 2: Since the reminder 6622 ≠ 0, we apply division lemma to 1915 and 6622, to get

6622 = 1915 x 3 + 877

Step 3: We consider the new divisor 1915 and the new remainder 877, and apply the division lemma to get

1915 = 877 x 2 + 161

We consider the new divisor 877 and the new remainder 161,and apply the division lemma to get

877 = 161 x 5 + 72

We consider the new divisor 161 and the new remainder 72,and apply the division lemma to get

161 = 72 x 2 + 17

We consider the new divisor 72 and the new remainder 17,and apply the division lemma to get

72 = 17 x 4 + 4

We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get

17 = 4 x 4 + 1

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 8537 and 6622 is 1

Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(72,17) = HCF(161,72) = HCF(877,161) = HCF(1915,877) = HCF(6622,1915) = HCF(8537,6622) .

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

Step 1: Since 17146 > 1, we apply the division lemma to 17146 and 1, to get

17146 = 1 x 17146 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 17146 is 1

Notice that 1 = HCF(17146,1) .

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Frequently Asked Questions on HCF of 8537, 6622, 17146 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 8537, 6622, 17146?

Answer: HCF of 8537, 6622, 17146 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8537, 6622, 17146 using Euclid's Algorithm?

Answer: For arbitrary numbers 8537, 6622, 17146 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.