Highest Common Factor of 808, 2137, 6615 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 808, 2137, 6615 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 808, 2137, 6615 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 808, 2137, 6615 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 808, 2137, 6615 is 1.

HCF(808, 2137, 6615) = 1

HCF of 808, 2137, 6615 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 808, 2137, 6615 is 1.

Highest Common Factor of 808,2137,6615 using Euclid's algorithm

Highest Common Factor of 808,2137,6615 is 1

Step 1: Since 2137 > 808, we apply the division lemma to 2137 and 808, to get

2137 = 808 x 2 + 521

Step 2: Since the reminder 808 ≠ 0, we apply division lemma to 521 and 808, to get

808 = 521 x 1 + 287

Step 3: We consider the new divisor 521 and the new remainder 287, and apply the division lemma to get

521 = 287 x 1 + 234

We consider the new divisor 287 and the new remainder 234,and apply the division lemma to get

287 = 234 x 1 + 53

We consider the new divisor 234 and the new remainder 53,and apply the division lemma to get

234 = 53 x 4 + 22

We consider the new divisor 53 and the new remainder 22,and apply the division lemma to get

53 = 22 x 2 + 9

We consider the new divisor 22 and the new remainder 9,and apply the division lemma to get

22 = 9 x 2 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 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 808 and 2137 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(22,9) = HCF(53,22) = HCF(234,53) = HCF(287,234) = HCF(521,287) = HCF(808,521) = HCF(2137,808) .

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

Step 1: Since 6615 > 1, we apply the division lemma to 6615 and 1, to get

6615 = 1 x 6615 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6615 is 1

Notice that 1 = HCF(6615,1) .

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Frequently Asked Questions on HCF of 808, 2137, 6615 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 808, 2137, 6615?

Answer: HCF of 808, 2137, 6615 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 808, 2137, 6615 using Euclid's Algorithm?

Answer: For arbitrary numbers 808, 2137, 6615 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.