Highest Common Factor of 386, 746 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 386, 746 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 386, 746 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 386, 746 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 386, 746 is 2.

HCF(386, 746) = 2

HCF of 386, 746 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 386, 746 is 2.

Highest Common Factor of 386,746 using Euclid's algorithm

Highest Common Factor of 386,746 is 2

Step 1: Since 746 > 386, we apply the division lemma to 746 and 386, to get

746 = 386 x 1 + 360

Step 2: Since the reminder 386 ≠ 0, we apply division lemma to 360 and 386, to get

386 = 360 x 1 + 26

Step 3: We consider the new divisor 360 and the new remainder 26, and apply the division lemma to get

360 = 26 x 13 + 22

We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get

26 = 22 x 1 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 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 386 and 746 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(360,26) = HCF(386,360) = HCF(746,386) .

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Frequently Asked Questions on HCF of 386, 746 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 386, 746?

Answer: HCF of 386, 746 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 386, 746 using Euclid's Algorithm?

Answer: For arbitrary numbers 386, 746 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.