Highest Common Factor of 8208, 6300, 13222 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 8208, 6300, 13222 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 8208, 6300, 13222 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 8208, 6300, 13222 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 8208, 6300, 13222 is 2.

HCF(8208, 6300, 13222) = 2

HCF of 8208, 6300, 13222 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 8208, 6300, 13222 is 2.

Highest Common Factor of 8208,6300,13222 using Euclid's algorithm

Highest Common Factor of 8208,6300,13222 is 2

Step 1: Since 8208 > 6300, we apply the division lemma to 8208 and 6300, to get

8208 = 6300 x 1 + 1908

Step 2: Since the reminder 6300 ≠ 0, we apply division lemma to 1908 and 6300, to get

6300 = 1908 x 3 + 576

Step 3: We consider the new divisor 1908 and the new remainder 576, and apply the division lemma to get

1908 = 576 x 3 + 180

We consider the new divisor 576 and the new remainder 180,and apply the division lemma to get

576 = 180 x 3 + 36

We consider the new divisor 180 and the new remainder 36,and apply the division lemma to get

180 = 36 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 8208 and 6300 is 36

Notice that 36 = HCF(180,36) = HCF(576,180) = HCF(1908,576) = HCF(6300,1908) = HCF(8208,6300) .

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

Step 1: Since 13222 > 36, we apply the division lemma to 13222 and 36, to get

13222 = 36 x 367 + 10

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 10 and 36, to get

36 = 10 x 3 + 6

Step 3: 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 36 and 13222 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(36,10) = HCF(13222,36) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 8208, 6300, 13222 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 8208, 6300, 13222?

Answer: HCF of 8208, 6300, 13222 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8208, 6300, 13222 using Euclid's Algorithm?

Answer: For arbitrary numbers 8208, 6300, 13222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.