Highest Common Factor of 651, 504, 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 651, 504, 622 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 651, 504, 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 651, 504, 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 651, 504, 622 is 1.

HCF(651, 504, 622) = 1

HCF of 651, 504, 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 651, 504, 622 is 1.

Highest Common Factor of 651,504,622 using Euclid's algorithm

Highest Common Factor of 651,504,622 is 1

Step 1: Since 651 > 504, we apply the division lemma to 651 and 504, to get

651 = 504 x 1 + 147

Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 147 and 504, to get

504 = 147 x 3 + 63

Step 3: We consider the new divisor 147 and the new remainder 63, and apply the division lemma to get

147 = 63 x 2 + 21

We consider the new divisor 63 and the new remainder 21, and apply the division lemma to get

63 = 21 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 651 and 504 is 21

Notice that 21 = HCF(63,21) = HCF(147,63) = HCF(504,147) = HCF(651,504) .

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

Step 1: Since 622 > 21, we apply the division lemma to 622 and 21, to get

622 = 21 x 29 + 13

Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 13 and 21, to get

21 = 13 x 1 + 8

Step 3: We consider the new divisor 13 and the new remainder 8, and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 21 and 622 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(622,21) .

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Frequently Asked Questions on HCF of 651, 504, 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 651, 504, 622?

Answer: HCF of 651, 504, 622 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 651, 504, 622 using Euclid's Algorithm?

Answer: For arbitrary numbers 651, 504, 622 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.