Highest Common Factor of 1842, 8088, 82717 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 1842, 8088, 82717 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1842, 8088, 82717 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 1842, 8088, 82717 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 1842, 8088, 82717 is 1.

HCF(1842, 8088, 82717) = 1

HCF of 1842, 8088, 82717 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 1842, 8088, 82717 is 1.

Highest Common Factor of 1842,8088,82717 using Euclid's algorithm

Highest Common Factor of 1842,8088,82717 is 1

Step 1: Since 8088 > 1842, we apply the division lemma to 8088 and 1842, to get

8088 = 1842 x 4 + 720

Step 2: Since the reminder 1842 ≠ 0, we apply division lemma to 720 and 1842, to get

1842 = 720 x 2 + 402

Step 3: We consider the new divisor 720 and the new remainder 402, and apply the division lemma to get

720 = 402 x 1 + 318

We consider the new divisor 402 and the new remainder 318,and apply the division lemma to get

402 = 318 x 1 + 84

We consider the new divisor 318 and the new remainder 84,and apply the division lemma to get

318 = 84 x 3 + 66

We consider the new divisor 84 and the new remainder 66,and apply the division lemma to get

84 = 66 x 1 + 18

We consider the new divisor 66 and the new remainder 18,and apply the division lemma to get

66 = 18 x 3 + 12

We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get

18 = 12 x 1 + 6

We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 1842 and 8088 is 6

Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(66,18) = HCF(84,66) = HCF(318,84) = HCF(402,318) = HCF(720,402) = HCF(1842,720) = HCF(8088,1842) .

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

Step 1: Since 82717 > 6, we apply the division lemma to 82717 and 6, to get

82717 = 6 x 13786 + 1

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, 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 6 and 82717 is 1

Notice that 1 = HCF(6,1) = HCF(82717,6) .

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Frequently Asked Questions on HCF of 1842, 8088, 82717 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 1842, 8088, 82717?

Answer: HCF of 1842, 8088, 82717 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1842, 8088, 82717 using Euclid's Algorithm?

Answer: For arbitrary numbers 1842, 8088, 82717 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.