Highest Common Factor of 1651, 6522, 22756 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 1651, 6522, 22756 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1651, 6522, 22756 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 1651, 6522, 22756 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 1651, 6522, 22756 is 1.

HCF(1651, 6522, 22756) = 1

HCF of 1651, 6522, 22756 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 1651, 6522, 22756 is 1.

Highest Common Factor of 1651,6522,22756 using Euclid's algorithm

Highest Common Factor of 1651,6522,22756 is 1

Step 1: Since 6522 > 1651, we apply the division lemma to 6522 and 1651, to get

6522 = 1651 x 3 + 1569

Step 2: Since the reminder 1651 ≠ 0, we apply division lemma to 1569 and 1651, to get

1651 = 1569 x 1 + 82

Step 3: We consider the new divisor 1569 and the new remainder 82, and apply the division lemma to get

1569 = 82 x 19 + 11

We consider the new divisor 82 and the new remainder 11,and apply the division lemma to get

82 = 11 x 7 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 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 1651 and 6522 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(82,11) = HCF(1569,82) = HCF(1651,1569) = HCF(6522,1651) .

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

Step 1: Since 22756 > 1, we apply the division lemma to 22756 and 1, to get

22756 = 1 x 22756 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 22756 is 1

Notice that 1 = HCF(22756,1) .

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Frequently Asked Questions on HCF of 1651, 6522, 22756 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 1651, 6522, 22756?

Answer: HCF of 1651, 6522, 22756 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1651, 6522, 22756 using Euclid's Algorithm?

Answer: For arbitrary numbers 1651, 6522, 22756 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.