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

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

HCF(638, 386) = 2

HCF of 638, 386 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 638, 386 is 2.

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

Highest Common Factor of 638,386 is 2

Step 1: Since 638 > 386, we apply the division lemma to 638 and 386, to get

638 = 386 x 1 + 252

Step 2: Since the reminder 386 ≠ 0, we apply division lemma to 252 and 386, to get

386 = 252 x 1 + 134

Step 3: We consider the new divisor 252 and the new remainder 134, and apply the division lemma to get

252 = 134 x 1 + 118

We consider the new divisor 134 and the new remainder 118,and apply the division lemma to get

134 = 118 x 1 + 16

We consider the new divisor 118 and the new remainder 16,and apply the division lemma to get

118 = 16 x 7 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 638 and 386 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(118,16) = HCF(134,118) = HCF(252,134) = HCF(386,252) = HCF(638,386) .

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

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

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

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