Highest Common Factor of 677, 490, 644 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 677, 490, 644 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 677, 490, 644 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 677, 490, 644 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 677, 490, 644 is 1.

HCF(677, 490, 644) = 1

HCF of 677, 490, 644 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 677, 490, 644 is 1.

Highest Common Factor of 677,490,644 using Euclid's algorithm

Highest Common Factor of 677,490,644 is 1

Step 1: Since 677 > 490, we apply the division lemma to 677 and 490, to get

677 = 490 x 1 + 187

Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 187 and 490, to get

490 = 187 x 2 + 116

Step 3: We consider the new divisor 187 and the new remainder 116, and apply the division lemma to get

187 = 116 x 1 + 71

We consider the new divisor 116 and the new remainder 71,and apply the division lemma to get

116 = 71 x 1 + 45

We consider the new divisor 71 and the new remainder 45,and apply the division lemma to get

71 = 45 x 1 + 26

We consider the new divisor 45 and the new remainder 26,and apply the division lemma to get

45 = 26 x 1 + 19

We consider the new divisor 26 and the new remainder 19,and apply the division lemma to get

26 = 19 x 1 + 7

We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get

19 = 7 x 2 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 677 and 490 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(26,19) = HCF(45,26) = HCF(71,45) = HCF(116,71) = HCF(187,116) = HCF(490,187) = HCF(677,490) .

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

Step 1: Since 644 > 1, we apply the division lemma to 644 and 1, to get

644 = 1 x 644 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 644 is 1

Notice that 1 = HCF(644,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 677, 490, 644 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 677, 490, 644?

Answer: HCF of 677, 490, 644 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 677, 490, 644 using Euclid's Algorithm?

Answer: For arbitrary numbers 677, 490, 644 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.