Highest Common Factor of 643, 411, 566, 491 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, 411, 566, 491 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 643, 411, 566, 491 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, 411, 566, 491 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, 411, 566, 491 is 1.

HCF(643, 411, 566, 491) = 1

HCF of 643, 411, 566, 491 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, 411, 566, 491 is 1.

Highest Common Factor of 643,411,566,491 using Euclid's algorithm

Highest Common Factor of 643,411,566,491 is 1

Step 1: Since 643 > 411, we apply the division lemma to 643 and 411, to get

643 = 411 x 1 + 232

Step 2: Since the reminder 411 ≠ 0, we apply division lemma to 232 and 411, to get

411 = 232 x 1 + 179

Step 3: We consider the new divisor 232 and the new remainder 179, and apply the division lemma to get

232 = 179 x 1 + 53

We consider the new divisor 179 and the new remainder 53,and apply the division lemma to get

179 = 53 x 3 + 20

We consider the new divisor 53 and the new remainder 20,and apply the division lemma to get

53 = 20 x 2 + 13

We consider the new divisor 20 and the new remainder 13,and apply the division lemma to get

20 = 13 x 1 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 643 and 411 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(53,20) = HCF(179,53) = HCF(232,179) = HCF(411,232) = HCF(643,411) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 566 > 1, we apply the division lemma to 566 and 1, to get

566 = 1 x 566 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 566 is 1

Notice that 1 = HCF(566,1) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 491 > 1, we apply the division lemma to 491 and 1, to get

491 = 1 x 491 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 491 is 1

Notice that 1 = HCF(491,1) .

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, 411, 566, 491 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, 411, 566, 491?

Answer: HCF of 643, 411, 566, 491 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 643, 411, 566, 491 using Euclid's Algorithm?

Answer: For arbitrary numbers 643, 411, 566, 491 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.