Highest Common Factor of 643, 400 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 643, 400 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 643, 400 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 643, 400 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 643, 400 is 1.

HCF(643, 400) = 1

HCF of 643, 400 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 643, 400 is 1.

Highest Common Factor of 643,400 using Euclid's algorithm

Highest Common Factor of 643,400 is 1

Step 1: Since 643 > 400, we apply the division lemma to 643 and 400, to get

643 = 400 x 1 + 243

Step 2: Since the reminder 400 ≠ 0, we apply division lemma to 243 and 400, to get

400 = 243 x 1 + 157

Step 3: We consider the new divisor 243 and the new remainder 157, and apply the division lemma to get

243 = 157 x 1 + 86

We consider the new divisor 157 and the new remainder 86,and apply the division lemma to get

157 = 86 x 1 + 71

We consider the new divisor 86 and the new remainder 71,and apply the division lemma to get

86 = 71 x 1 + 15

We consider the new divisor 71 and the new remainder 15,and apply the division lemma to get

71 = 15 x 4 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 643 and 400 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(71,15) = HCF(86,71) = HCF(157,86) = HCF(243,157) = HCF(400,243) = HCF(643,400) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 643, 400 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 643, 400?

Answer: HCF of 643, 400 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 643, 400 using Euclid's Algorithm?

Answer: For arbitrary numbers 643, 400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.