Highest Common Factor of 6998, 2605, 86489 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 6998, 2605, 86489 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6998, 2605, 86489 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 6998, 2605, 86489 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 6998, 2605, 86489 is 1.

HCF(6998, 2605, 86489) = 1

HCF of 6998, 2605, 86489 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 6998, 2605, 86489 is 1.

Highest Common Factor of 6998,2605,86489 using Euclid's algorithm

Highest Common Factor of 6998,2605,86489 is 1

Step 1: Since 6998 > 2605, we apply the division lemma to 6998 and 2605, to get

6998 = 2605 x 2 + 1788

Step 2: Since the reminder 2605 ≠ 0, we apply division lemma to 1788 and 2605, to get

2605 = 1788 x 1 + 817

Step 3: We consider the new divisor 1788 and the new remainder 817, and apply the division lemma to get

1788 = 817 x 2 + 154

We consider the new divisor 817 and the new remainder 154,and apply the division lemma to get

817 = 154 x 5 + 47

We consider the new divisor 154 and the new remainder 47,and apply the division lemma to get

154 = 47 x 3 + 13

We consider the new divisor 47 and the new remainder 13,and apply the division lemma to get

47 = 13 x 3 + 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 6998 and 2605 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(47,13) = HCF(154,47) = HCF(817,154) = HCF(1788,817) = HCF(2605,1788) = HCF(6998,2605) .

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

Step 1: Since 86489 > 1, we apply the division lemma to 86489 and 1, to get

86489 = 1 x 86489 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 86489 is 1

Notice that 1 = HCF(86489,1) .

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Frequently Asked Questions on HCF of 6998, 2605, 86489 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 6998, 2605, 86489?

Answer: HCF of 6998, 2605, 86489 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6998, 2605, 86489 using Euclid's Algorithm?

Answer: For arbitrary numbers 6998, 2605, 86489 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.