Highest Common Factor of 8181, 1724 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 8181, 1724 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8181, 1724 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 8181, 1724 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 8181, 1724 is 1.

HCF(8181, 1724) = 1

HCF of 8181, 1724 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 8181, 1724 is 1.

Highest Common Factor of 8181,1724 using Euclid's algorithm

Highest Common Factor of 8181,1724 is 1

Step 1: Since 8181 > 1724, we apply the division lemma to 8181 and 1724, to get

8181 = 1724 x 4 + 1285

Step 2: Since the reminder 1724 ≠ 0, we apply division lemma to 1285 and 1724, to get

1724 = 1285 x 1 + 439

Step 3: We consider the new divisor 1285 and the new remainder 439, and apply the division lemma to get

1285 = 439 x 2 + 407

We consider the new divisor 439 and the new remainder 407,and apply the division lemma to get

439 = 407 x 1 + 32

We consider the new divisor 407 and the new remainder 32,and apply the division lemma to get

407 = 32 x 12 + 23

We consider the new divisor 32 and the new remainder 23,and apply the division lemma to get

32 = 23 x 1 + 9

We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get

23 = 9 x 2 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8181 and 1724 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(32,23) = HCF(407,32) = HCF(439,407) = HCF(1285,439) = HCF(1724,1285) = HCF(8181,1724) .

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Frequently Asked Questions on HCF of 8181, 1724 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 8181, 1724?

Answer: HCF of 8181, 1724 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8181, 1724 using Euclid's Algorithm?

Answer: For arbitrary numbers 8181, 1724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.