Highest Common Factor of 6812, 6370, 43652 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 6812, 6370, 43652 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 6812, 6370, 43652 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 6812, 6370, 43652 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 6812, 6370, 43652 is 2.

HCF(6812, 6370, 43652) = 2

HCF of 6812, 6370, 43652 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 6812, 6370, 43652 is 2.

Highest Common Factor of 6812,6370,43652 using Euclid's algorithm

Highest Common Factor of 6812,6370,43652 is 2

Step 1: Since 6812 > 6370, we apply the division lemma to 6812 and 6370, to get

6812 = 6370 x 1 + 442

Step 2: Since the reminder 6370 ≠ 0, we apply division lemma to 442 and 6370, to get

6370 = 442 x 14 + 182

Step 3: We consider the new divisor 442 and the new remainder 182, and apply the division lemma to get

442 = 182 x 2 + 78

We consider the new divisor 182 and the new remainder 78,and apply the division lemma to get

182 = 78 x 2 + 26

We consider the new divisor 78 and the new remainder 26,and apply the division lemma to get

78 = 26 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 6812 and 6370 is 26

Notice that 26 = HCF(78,26) = HCF(182,78) = HCF(442,182) = HCF(6370,442) = HCF(6812,6370) .

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

Step 1: Since 43652 > 26, we apply the division lemma to 43652 and 26, to get

43652 = 26 x 1678 + 24

Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 24 and 26, to get

26 = 24 x 1 + 2

Step 3: We consider the new divisor 24 and the new remainder 2, and apply the division lemma to get

24 = 2 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 26 and 43652 is 2

Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(43652,26) .

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Frequently Asked Questions on HCF of 6812, 6370, 43652 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 6812, 6370, 43652?

Answer: HCF of 6812, 6370, 43652 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6812, 6370, 43652 using Euclid's Algorithm?

Answer: For arbitrary numbers 6812, 6370, 43652 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.