Highest Common Factor of 470, 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 470, 643 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 470, 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 470, 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 470, 643 is 1.

HCF(470, 643) = 1

HCF of 470, 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 470, 643 is 1.

Highest Common Factor of 470,643 using Euclid's algorithm

Highest Common Factor of 470,643 is 1

Step 1: Since 643 > 470, we apply the division lemma to 643 and 470, to get

643 = 470 x 1 + 173

Step 2: Since the reminder 470 ≠ 0, we apply division lemma to 173 and 470, to get

470 = 173 x 2 + 124

Step 3: We consider the new divisor 173 and the new remainder 124, and apply the division lemma to get

173 = 124 x 1 + 49

We consider the new divisor 124 and the new remainder 49,and apply the division lemma to get

124 = 49 x 2 + 26

We consider the new divisor 49 and the new remainder 26,and apply the division lemma to get

49 = 26 x 1 + 23

We consider the new divisor 26 and the new remainder 23,and apply the division lemma to get

26 = 23 x 1 + 3

We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get

23 = 3 x 7 + 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 470 and 643 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(26,23) = HCF(49,26) = HCF(124,49) = HCF(173,124) = HCF(470,173) = HCF(643,470) .

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Frequently Asked Questions on HCF of 470, 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 470, 643?

Answer: HCF of 470, 643 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 470, 643 using Euclid's Algorithm?

Answer: For arbitrary numbers 470, 643 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.