Highest Common Factor of 8172, 2491, 41217 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 8172, 2491, 41217 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8172, 2491, 41217 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 8172, 2491, 41217 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 8172, 2491, 41217 is 1.

HCF(8172, 2491, 41217) = 1

HCF of 8172, 2491, 41217 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 8172, 2491, 41217 is 1.

Highest Common Factor of 8172,2491,41217 using Euclid's algorithm

Highest Common Factor of 8172,2491,41217 is 1

Step 1: Since 8172 > 2491, we apply the division lemma to 8172 and 2491, to get

8172 = 2491 x 3 + 699

Step 2: Since the reminder 2491 ≠ 0, we apply division lemma to 699 and 2491, to get

2491 = 699 x 3 + 394

Step 3: We consider the new divisor 699 and the new remainder 394, and apply the division lemma to get

699 = 394 x 1 + 305

We consider the new divisor 394 and the new remainder 305,and apply the division lemma to get

394 = 305 x 1 + 89

We consider the new divisor 305 and the new remainder 89,and apply the division lemma to get

305 = 89 x 3 + 38

We consider the new divisor 89 and the new remainder 38,and apply the division lemma to get

89 = 38 x 2 + 13

We consider the new divisor 38 and the new remainder 13,and apply the division lemma to get

38 = 13 x 2 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8172 and 2491 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(38,13) = HCF(89,38) = HCF(305,89) = HCF(394,305) = HCF(699,394) = HCF(2491,699) = HCF(8172,2491) .

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

Step 1: Since 41217 > 1, we apply the division lemma to 41217 and 1, to get

41217 = 1 x 41217 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 41217 is 1

Notice that 1 = HCF(41217,1) .

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Frequently Asked Questions on HCF of 8172, 2491, 41217 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 8172, 2491, 41217?

Answer: HCF of 8172, 2491, 41217 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8172, 2491, 41217 using Euclid's Algorithm?

Answer: For arbitrary numbers 8172, 2491, 41217 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.