Highest Common Factor of 756, 987, 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 756, 987, 622 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 756, 987, 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 756, 987, 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 756, 987, 622 is 1.

HCF(756, 987, 622) = 1

HCF of 756, 987, 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 756, 987, 622 is 1.

Highest Common Factor of 756,987,622 using Euclid's algorithm

Highest Common Factor of 756,987,622 is 1

Step 1: Since 987 > 756, we apply the division lemma to 987 and 756, to get

987 = 756 x 1 + 231

Step 2: Since the reminder 756 ≠ 0, we apply division lemma to 231 and 756, to get

756 = 231 x 3 + 63

Step 3: We consider the new divisor 231 and the new remainder 63, and apply the division lemma to get

231 = 63 x 3 + 42

We consider the new divisor 63 and the new remainder 42,and apply the division lemma to get

63 = 42 x 1 + 21

We consider the new divisor 42 and the new remainder 21,and apply the division lemma to get

42 = 21 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 756 and 987 is 21

Notice that 21 = HCF(42,21) = HCF(63,42) = HCF(231,63) = HCF(756,231) = HCF(987,756) .

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 756, 987, 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 756, 987, 622?

Answer: HCF of 756, 987, 622 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 756, 987, 622 using Euclid's Algorithm?

Answer: For arbitrary numbers 756, 987, 622 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.