Highest Common Factor of 8716, 6525, 22119 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 8716, 6525, 22119 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8716, 6525, 22119 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 8716, 6525, 22119 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 8716, 6525, 22119 is 1.

HCF(8716, 6525, 22119) = 1

HCF of 8716, 6525, 22119 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 8716, 6525, 22119 is 1.

Highest Common Factor of 8716,6525,22119 using Euclid's algorithm

Highest Common Factor of 8716,6525,22119 is 1

Step 1: Since 8716 > 6525, we apply the division lemma to 8716 and 6525, to get

8716 = 6525 x 1 + 2191

Step 2: Since the reminder 6525 ≠ 0, we apply division lemma to 2191 and 6525, to get

6525 = 2191 x 2 + 2143

Step 3: We consider the new divisor 2191 and the new remainder 2143, and apply the division lemma to get

2191 = 2143 x 1 + 48

We consider the new divisor 2143 and the new remainder 48,and apply the division lemma to get

2143 = 48 x 44 + 31

We consider the new divisor 48 and the new remainder 31,and apply the division lemma to get

48 = 31 x 1 + 17

We consider the new divisor 31 and the new remainder 17,and apply the division lemma to get

31 = 17 x 1 + 14

We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get

17 = 14 x 1 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 2

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

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8716 and 6525 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(31,17) = HCF(48,31) = HCF(2143,48) = HCF(2191,2143) = HCF(6525,2191) = HCF(8716,6525) .

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

Step 1: Since 22119 > 1, we apply the division lemma to 22119 and 1, to get

22119 = 1 x 22119 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 22119 is 1

Notice that 1 = HCF(22119,1) .

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Frequently Asked Questions on HCF of 8716, 6525, 22119 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 8716, 6525, 22119?

Answer: HCF of 8716, 6525, 22119 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8716, 6525, 22119 using Euclid's Algorithm?

Answer: For arbitrary numbers 8716, 6525, 22119 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.