Highest Common Factor of 822, 645, 551 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 822, 645, 551 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 822, 645, 551 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 822, 645, 551 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 822, 645, 551 is 1.

HCF(822, 645, 551) = 1

HCF of 822, 645, 551 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 822, 645, 551 is 1.

Highest Common Factor of 822,645,551 using Euclid's algorithm

Highest Common Factor of 822,645,551 is 1

Step 1: Since 822 > 645, we apply the division lemma to 822 and 645, to get

822 = 645 x 1 + 177

Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 177 and 645, to get

645 = 177 x 3 + 114

Step 3: We consider the new divisor 177 and the new remainder 114, and apply the division lemma to get

177 = 114 x 1 + 63

We consider the new divisor 114 and the new remainder 63,and apply the division lemma to get

114 = 63 x 1 + 51

We consider the new divisor 63 and the new remainder 51,and apply the division lemma to get

63 = 51 x 1 + 12

We consider the new divisor 51 and the new remainder 12,and apply the division lemma to get

51 = 12 x 4 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 822 and 645 is 3

Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(63,51) = HCF(114,63) = HCF(177,114) = HCF(645,177) = HCF(822,645) .

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

Step 1: Since 551 > 3, we apply the division lemma to 551 and 3, to get

551 = 3 x 183 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 551 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(551,3) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 822, 645, 551 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 822, 645, 551?

Answer: HCF of 822, 645, 551 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 822, 645, 551 using Euclid's Algorithm?

Answer: For arbitrary numbers 822, 645, 551 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.