Highest Common Factor of 2202, 8269, 55692 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 2202, 8269, 55692 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2202, 8269, 55692 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 2202, 8269, 55692 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 2202, 8269, 55692 is 1.

HCF(2202, 8269, 55692) = 1

HCF of 2202, 8269, 55692 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 2202, 8269, 55692 is 1.

Highest Common Factor of 2202,8269,55692 using Euclid's algorithm

Highest Common Factor of 2202,8269,55692 is 1

Step 1: Since 8269 > 2202, we apply the division lemma to 8269 and 2202, to get

8269 = 2202 x 3 + 1663

Step 2: Since the reminder 2202 ≠ 0, we apply division lemma to 1663 and 2202, to get

2202 = 1663 x 1 + 539

Step 3: We consider the new divisor 1663 and the new remainder 539, and apply the division lemma to get

1663 = 539 x 3 + 46

We consider the new divisor 539 and the new remainder 46,and apply the division lemma to get

539 = 46 x 11 + 33

We consider the new divisor 46 and the new remainder 33,and apply the division lemma to get

46 = 33 x 1 + 13

We consider the new divisor 33 and the new remainder 13,and apply the division lemma to get

33 = 13 x 2 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2202 and 8269 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(33,13) = HCF(46,33) = HCF(539,46) = HCF(1663,539) = HCF(2202,1663) = HCF(8269,2202) .

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

Step 1: Since 55692 > 1, we apply the division lemma to 55692 and 1, to get

55692 = 1 x 55692 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 55692 is 1

Notice that 1 = HCF(55692,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 2202, 8269, 55692 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 2202, 8269, 55692?

Answer: HCF of 2202, 8269, 55692 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2202, 8269, 55692 using Euclid's Algorithm?

Answer: For arbitrary numbers 2202, 8269, 55692 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.