Highest Common Factor of 278, 386, 638 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 278, 386, 638 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 278, 386, 638 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 278, 386, 638 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 278, 386, 638 is 2.

HCF(278, 386, 638) = 2

HCF of 278, 386, 638 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 278, 386, 638 is 2.

Highest Common Factor of 278,386,638 using Euclid's algorithm

Highest Common Factor of 278,386,638 is 2

Step 1: Since 386 > 278, we apply the division lemma to 386 and 278, to get

386 = 278 x 1 + 108

Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 108 and 278, to get

278 = 108 x 2 + 62

Step 3: We consider the new divisor 108 and the new remainder 62, and apply the division lemma to get

108 = 62 x 1 + 46

We consider the new divisor 62 and the new remainder 46,and apply the division lemma to get

62 = 46 x 1 + 16

We consider the new divisor 46 and the new remainder 16,and apply the division lemma to get

46 = 16 x 2 + 14

We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get

16 = 14 x 1 + 2

We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 278 and 386 is 2

Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(46,16) = HCF(62,46) = HCF(108,62) = HCF(278,108) = HCF(386,278) .

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

Step 1: Since 638 > 2, we apply the division lemma to 638 and 2, to get

638 = 2 x 319 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 638 is 2

Notice that 2 = HCF(638,2) .

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Frequently Asked Questions on HCF of 278, 386, 638 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 278, 386, 638?

Answer: HCF of 278, 386, 638 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 278, 386, 638 using Euclid's Algorithm?

Answer: For arbitrary numbers 278, 386, 638 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.