Highest Common Factor of 642, 282, 204 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 642, 282, 204 i.e. 6 the largest integer that leaves a remainder zero for all numbers.

HCF of 642, 282, 204 is 6 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 642, 282, 204 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 642, 282, 204 is 6.

HCF(642, 282, 204) = 6

HCF of 642, 282, 204 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 642, 282, 204 is 6.

Highest Common Factor of 642,282,204 using Euclid's algorithm

Highest Common Factor of 642,282,204 is 6

Step 1: Since 642 > 282, we apply the division lemma to 642 and 282, to get

642 = 282 x 2 + 78

Step 2: Since the reminder 282 ≠ 0, we apply division lemma to 78 and 282, to get

282 = 78 x 3 + 48

Step 3: We consider the new divisor 78 and the new remainder 48, and apply the division lemma to get

78 = 48 x 1 + 30

We consider the new divisor 48 and the new remainder 30,and apply the division lemma to get

48 = 30 x 1 + 18

We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get

30 = 18 x 1 + 12

We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get

18 = 12 x 1 + 6

We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 642 and 282 is 6

Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(48,30) = HCF(78,48) = HCF(282,78) = HCF(642,282) .

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

Step 1: Since 204 > 6, we apply the division lemma to 204 and 6, to get

204 = 6 x 34 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 204 is 6

Notice that 6 = HCF(204,6) .

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Frequently Asked Questions on HCF of 642, 282, 204 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 642, 282, 204?

Answer: HCF of 642, 282, 204 is 6 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 642, 282, 204 using Euclid's Algorithm?

Answer: For arbitrary numbers 642, 282, 204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.