Highest Common Factor of 2242, 7131, 18032 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 2242, 7131, 18032 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2242, 7131, 18032 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 2242, 7131, 18032 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 2242, 7131, 18032 is 1.

HCF(2242, 7131, 18032) = 1

HCF of 2242, 7131, 18032 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 2242, 7131, 18032 is 1.

Highest Common Factor of 2242,7131,18032 using Euclid's algorithm

Highest Common Factor of 2242,7131,18032 is 1

Step 1: Since 7131 > 2242, we apply the division lemma to 7131 and 2242, to get

7131 = 2242 x 3 + 405

Step 2: Since the reminder 2242 ≠ 0, we apply division lemma to 405 and 2242, to get

2242 = 405 x 5 + 217

Step 3: We consider the new divisor 405 and the new remainder 217, and apply the division lemma to get

405 = 217 x 1 + 188

We consider the new divisor 217 and the new remainder 188,and apply the division lemma to get

217 = 188 x 1 + 29

We consider the new divisor 188 and the new remainder 29,and apply the division lemma to get

188 = 29 x 6 + 14

We consider the new divisor 29 and the new remainder 14,and apply the division lemma to get

29 = 14 x 2 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2242 and 7131 is 1

Notice that 1 = HCF(14,1) = HCF(29,14) = HCF(188,29) = HCF(217,188) = HCF(405,217) = HCF(2242,405) = HCF(7131,2242) .

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

Step 1: Since 18032 > 1, we apply the division lemma to 18032 and 1, to get

18032 = 1 x 18032 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 18032 is 1

Notice that 1 = HCF(18032,1) .

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Frequently Asked Questions on HCF of 2242, 7131, 18032 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 2242, 7131, 18032?

Answer: HCF of 2242, 7131, 18032 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2242, 7131, 18032 using Euclid's Algorithm?

Answer: For arbitrary numbers 2242, 7131, 18032 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.