Highest Common Factor of 9971, 1722, 83805 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 9971, 1722, 83805 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9971, 1722, 83805 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 9971, 1722, 83805 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 9971, 1722, 83805 is 1.

HCF(9971, 1722, 83805) = 1

HCF of 9971, 1722, 83805 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 9971, 1722, 83805 is 1.

Highest Common Factor of 9971,1722,83805 using Euclid's algorithm

Highest Common Factor of 9971,1722,83805 is 1

Step 1: Since 9971 > 1722, we apply the division lemma to 9971 and 1722, to get

9971 = 1722 x 5 + 1361

Step 2: Since the reminder 1722 ≠ 0, we apply division lemma to 1361 and 1722, to get

1722 = 1361 x 1 + 361

Step 3: We consider the new divisor 1361 and the new remainder 361, and apply the division lemma to get

1361 = 361 x 3 + 278

We consider the new divisor 361 and the new remainder 278,and apply the division lemma to get

361 = 278 x 1 + 83

We consider the new divisor 278 and the new remainder 83,and apply the division lemma to get

278 = 83 x 3 + 29

We consider the new divisor 83 and the new remainder 29,and apply the division lemma to get

83 = 29 x 2 + 25

We consider the new divisor 29 and the new remainder 25,and apply the division lemma to get

29 = 25 x 1 + 4

We consider the new divisor 25 and the new remainder 4,and apply the division lemma to get

25 = 4 x 6 + 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 9971 and 1722 is 1

Notice that 1 = HCF(4,1) = HCF(25,4) = HCF(29,25) = HCF(83,29) = HCF(278,83) = HCF(361,278) = HCF(1361,361) = HCF(1722,1361) = HCF(9971,1722) .

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

Step 1: Since 83805 > 1, we apply the division lemma to 83805 and 1, to get

83805 = 1 x 83805 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 83805 is 1

Notice that 1 = HCF(83805,1) .

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Frequently Asked Questions on HCF of 9971, 1722, 83805 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 9971, 1722, 83805?

Answer: HCF of 9971, 1722, 83805 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9971, 1722, 83805 using Euclid's Algorithm?

Answer: For arbitrary numbers 9971, 1722, 83805 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.