Highest Common Factor of 639, 2416, 6364 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 639, 2416, 6364 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 639, 2416, 6364 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 639, 2416, 6364 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 639, 2416, 6364 is 1.

HCF(639, 2416, 6364) = 1

HCF of 639, 2416, 6364 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 639, 2416, 6364 is 1.

Highest Common Factor of 639,2416,6364 using Euclid's algorithm

Highest Common Factor of 639,2416,6364 is 1

Step 1: Since 2416 > 639, we apply the division lemma to 2416 and 639, to get

2416 = 639 x 3 + 499

Step 2: Since the reminder 639 ≠ 0, we apply division lemma to 499 and 639, to get

639 = 499 x 1 + 140

Step 3: We consider the new divisor 499 and the new remainder 140, and apply the division lemma to get

499 = 140 x 3 + 79

We consider the new divisor 140 and the new remainder 79,and apply the division lemma to get

140 = 79 x 1 + 61

We consider the new divisor 79 and the new remainder 61,and apply the division lemma to get

79 = 61 x 1 + 18

We consider the new divisor 61 and the new remainder 18,and apply the division lemma to get

61 = 18 x 3 + 7

We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get

18 = 7 x 2 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 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 639 and 2416 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(61,18) = HCF(79,61) = HCF(140,79) = HCF(499,140) = HCF(639,499) = HCF(2416,639) .

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

Step 1: Since 6364 > 1, we apply the division lemma to 6364 and 1, to get

6364 = 1 x 6364 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6364 is 1

Notice that 1 = HCF(6364,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 639, 2416, 6364 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 639, 2416, 6364?

Answer: HCF of 639, 2416, 6364 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 639, 2416, 6364 using Euclid's Algorithm?

Answer: For arbitrary numbers 639, 2416, 6364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.