Highest Common Factor of 362, 643 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 362, 643 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 362, 643 is 1 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 362, 643 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 362, 643 is 1.

HCF(362, 643) = 1

HCF of 362, 643 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 362, 643 is 1.

Highest Common Factor of 362,643 using Euclid's algorithm

Highest Common Factor of 362,643 is 1

Step 1: Since 643 > 362, we apply the division lemma to 643 and 362, to get

643 = 362 x 1 + 281

Step 2: Since the reminder 362 ≠ 0, we apply division lemma to 281 and 362, to get

362 = 281 x 1 + 81

Step 3: We consider the new divisor 281 and the new remainder 81, and apply the division lemma to get

281 = 81 x 3 + 38

We consider the new divisor 81 and the new remainder 38,and apply the division lemma to get

81 = 38 x 2 + 5

We consider the new divisor 38 and the new remainder 5,and apply the division lemma to get

38 = 5 x 7 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 362 and 643 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(38,5) = HCF(81,38) = HCF(281,81) = HCF(362,281) = HCF(643,362) .

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Frequently Asked Questions on HCF of 362, 643 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 362, 643?

Answer: HCF of 362, 643 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 362, 643 using Euclid's Algorithm?

Answer: For arbitrary numbers 362, 643 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.