Highest Common Factor of 643, 452, 516 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, 452, 516 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 643, 452, 516 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, 452, 516 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, 452, 516 is 1.

HCF(643, 452, 516) = 1

HCF of 643, 452, 516 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, 452, 516 is 1.

Highest Common Factor of 643,452,516 using Euclid's algorithm

Highest Common Factor of 643,452,516 is 1

Step 1: Since 643 > 452, we apply the division lemma to 643 and 452, to get

643 = 452 x 1 + 191

Step 2: Since the reminder 452 ≠ 0, we apply division lemma to 191 and 452, to get

452 = 191 x 2 + 70

Step 3: We consider the new divisor 191 and the new remainder 70, and apply the division lemma to get

191 = 70 x 2 + 51

We consider the new divisor 70 and the new remainder 51,and apply the division lemma to get

70 = 51 x 1 + 19

We consider the new divisor 51 and the new remainder 19,and apply the division lemma to get

51 = 19 x 2 + 13

We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get

19 = 13 x 1 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 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 452 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(51,19) = HCF(70,51) = HCF(191,70) = HCF(452,191) = HCF(643,452) .

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

Step 1: Since 516 > 1, we apply the division lemma to 516 and 1, to get

516 = 1 x 516 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 516 is 1

Notice that 1 = HCF(516,1) .

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, 452, 516 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, 452, 516?

Answer: HCF of 643, 452, 516 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 643, 452, 516 using Euclid's Algorithm?

Answer: For arbitrary numbers 643, 452, 516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.