Highest Common Factor of 5640, 8262, 37466 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 5640, 8262, 37466 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 5640, 8262, 37466 is 2 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 5640, 8262, 37466 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 5640, 8262, 37466 is 2.

HCF(5640, 8262, 37466) = 2

HCF of 5640, 8262, 37466 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 5640, 8262, 37466 is 2.

Highest Common Factor of 5640,8262,37466 using Euclid's algorithm

Highest Common Factor of 5640,8262,37466 is 2

Step 1: Since 8262 > 5640, we apply the division lemma to 8262 and 5640, to get

8262 = 5640 x 1 + 2622

Step 2: Since the reminder 5640 ≠ 0, we apply division lemma to 2622 and 5640, to get

5640 = 2622 x 2 + 396

Step 3: We consider the new divisor 2622 and the new remainder 396, and apply the division lemma to get

2622 = 396 x 6 + 246

We consider the new divisor 396 and the new remainder 246,and apply the division lemma to get

396 = 246 x 1 + 150

We consider the new divisor 246 and the new remainder 150,and apply the division lemma to get

246 = 150 x 1 + 96

We consider the new divisor 150 and the new remainder 96,and apply the division lemma to get

150 = 96 x 1 + 54

We consider the new divisor 96 and the new remainder 54,and apply the division lemma to get

96 = 54 x 1 + 42

We consider the new divisor 54 and the new remainder 42,and apply the division lemma to get

54 = 42 x 1 + 12

We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get

42 = 12 x 3 + 6

We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 5640 and 8262 is 6

Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(54,42) = HCF(96,54) = HCF(150,96) = HCF(246,150) = HCF(396,246) = HCF(2622,396) = HCF(5640,2622) = HCF(8262,5640) .

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

Step 1: Since 37466 > 6, we apply the division lemma to 37466 and 6, to get

37466 = 6 x 6244 + 2

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 37466 is 2

Notice that 2 = HCF(6,2) = HCF(37466,6) .

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Frequently Asked Questions on HCF of 5640, 8262, 37466 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 5640, 8262, 37466?

Answer: HCF of 5640, 8262, 37466 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5640, 8262, 37466 using Euclid's Algorithm?

Answer: For arbitrary numbers 5640, 8262, 37466 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.