Highest Common Factor of 618, 8362, 6754 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 618, 8362, 6754 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 618, 8362, 6754 is 2 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 618, 8362, 6754 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 618, 8362, 6754 is 2.

HCF(618, 8362, 6754) = 2

HCF of 618, 8362, 6754 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 618, 8362, 6754 is 2.

Highest Common Factor of 618,8362,6754 using Euclid's algorithm

Highest Common Factor of 618,8362,6754 is 2

Step 1: Since 8362 > 618, we apply the division lemma to 8362 and 618, to get

8362 = 618 x 13 + 328

Step 2: Since the reminder 618 ≠ 0, we apply division lemma to 328 and 618, to get

618 = 328 x 1 + 290

Step 3: We consider the new divisor 328 and the new remainder 290, and apply the division lemma to get

328 = 290 x 1 + 38

We consider the new divisor 290 and the new remainder 38,and apply the division lemma to get

290 = 38 x 7 + 24

We consider the new divisor 38 and the new remainder 24,and apply the division lemma to get

38 = 24 x 1 + 14

We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get

24 = 14 x 1 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 618 and 8362 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(38,24) = HCF(290,38) = HCF(328,290) = HCF(618,328) = HCF(8362,618) .

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

Step 1: Since 6754 > 2, we apply the division lemma to 6754 and 2, to get

6754 = 2 x 3377 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 6754 is 2

Notice that 2 = HCF(6754,2) .

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Frequently Asked Questions on HCF of 618, 8362, 6754 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 618, 8362, 6754?

Answer: HCF of 618, 8362, 6754 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 618, 8362, 6754 using Euclid's Algorithm?

Answer: For arbitrary numbers 618, 8362, 6754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.