Highest Common Factor of 2661, 1656, 11026 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 2661, 1656, 11026 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2661, 1656, 11026 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 2661, 1656, 11026 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 2661, 1656, 11026 is 1.

HCF(2661, 1656, 11026) = 1

HCF of 2661, 1656, 11026 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 2661, 1656, 11026 is 1.

Highest Common Factor of 2661,1656,11026 using Euclid's algorithm

Highest Common Factor of 2661,1656,11026 is 1

Step 1: Since 2661 > 1656, we apply the division lemma to 2661 and 1656, to get

2661 = 1656 x 1 + 1005

Step 2: Since the reminder 1656 ≠ 0, we apply division lemma to 1005 and 1656, to get

1656 = 1005 x 1 + 651

Step 3: We consider the new divisor 1005 and the new remainder 651, and apply the division lemma to get

1005 = 651 x 1 + 354

We consider the new divisor 651 and the new remainder 354,and apply the division lemma to get

651 = 354 x 1 + 297

We consider the new divisor 354 and the new remainder 297,and apply the division lemma to get

354 = 297 x 1 + 57

We consider the new divisor 297 and the new remainder 57,and apply the division lemma to get

297 = 57 x 5 + 12

We consider the new divisor 57 and the new remainder 12,and apply the division lemma to get

57 = 12 x 4 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2661 and 1656 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(57,12) = HCF(297,57) = HCF(354,297) = HCF(651,354) = HCF(1005,651) = HCF(1656,1005) = HCF(2661,1656) .

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

Step 1: Since 11026 > 3, we apply the division lemma to 11026 and 3, to get

11026 = 3 x 3675 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 11026 is 1

Notice that 1 = HCF(3,1) = HCF(11026,3) .

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Frequently Asked Questions on HCF of 2661, 1656, 11026 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 2661, 1656, 11026?

Answer: HCF of 2661, 1656, 11026 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2661, 1656, 11026 using Euclid's Algorithm?

Answer: For arbitrary numbers 2661, 1656, 11026 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.