Highest Common Factor of 771, 977, 622 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 771, 977, 622 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 771, 977, 622 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 771, 977, 622 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 771, 977, 622 is 1.

HCF(771, 977, 622) = 1

HCF of 771, 977, 622 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 771, 977, 622 is 1.

Highest Common Factor of 771,977,622 using Euclid's algorithm

Highest Common Factor of 771,977,622 is 1

Step 1: Since 977 > 771, we apply the division lemma to 977 and 771, to get

977 = 771 x 1 + 206

Step 2: Since the reminder 771 ≠ 0, we apply division lemma to 206 and 771, to get

771 = 206 x 3 + 153

Step 3: We consider the new divisor 206 and the new remainder 153, and apply the division lemma to get

206 = 153 x 1 + 53

We consider the new divisor 153 and the new remainder 53,and apply the division lemma to get

153 = 53 x 2 + 47

We consider the new divisor 53 and the new remainder 47,and apply the division lemma to get

53 = 47 x 1 + 6

We consider the new divisor 47 and the new remainder 6,and apply the division lemma to get

47 = 6 x 7 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 771 and 977 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(47,6) = HCF(53,47) = HCF(153,53) = HCF(206,153) = HCF(771,206) = HCF(977,771) .

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

Step 1: Since 622 > 1, we apply the division lemma to 622 and 1, to get

622 = 1 x 622 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 622 is 1

Notice that 1 = HCF(622,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 771, 977, 622 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 771, 977, 622?

Answer: HCF of 771, 977, 622 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 771, 977, 622 using Euclid's Algorithm?

Answer: For arbitrary numbers 771, 977, 622 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.