Highest Common Factor of 6324, 9914 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 6324, 9914 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 6324, 9914 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 6324, 9914 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 6324, 9914 is 2.

HCF(6324, 9914) = 2

HCF of 6324, 9914 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 6324, 9914 is 2.

Highest Common Factor of 6324,9914 using Euclid's algorithm

Highest Common Factor of 6324,9914 is 2

Step 1: Since 9914 > 6324, we apply the division lemma to 9914 and 6324, to get

9914 = 6324 x 1 + 3590

Step 2: Since the reminder 6324 ≠ 0, we apply division lemma to 3590 and 6324, to get

6324 = 3590 x 1 + 2734

Step 3: We consider the new divisor 3590 and the new remainder 2734, and apply the division lemma to get

3590 = 2734 x 1 + 856

We consider the new divisor 2734 and the new remainder 856,and apply the division lemma to get

2734 = 856 x 3 + 166

We consider the new divisor 856 and the new remainder 166,and apply the division lemma to get

856 = 166 x 5 + 26

We consider the new divisor 166 and the new remainder 26,and apply the division lemma to get

166 = 26 x 6 + 10

We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get

26 = 10 x 2 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6324 and 9914 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(166,26) = HCF(856,166) = HCF(2734,856) = HCF(3590,2734) = HCF(6324,3590) = HCF(9914,6324) .

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Frequently Asked Questions on HCF of 6324, 9914 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 6324, 9914?

Answer: HCF of 6324, 9914 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6324, 9914 using Euclid's Algorithm?

Answer: For arbitrary numbers 6324, 9914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.