Highest Common Factor of 2983, 8107 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 2983, 8107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2983, 8107 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 2983, 8107 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 2983, 8107 is 1.

HCF(2983, 8107) = 1

HCF of 2983, 8107 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 2983, 8107 is 1.

Highest Common Factor of 2983,8107 using Euclid's algorithm

Highest Common Factor of 2983,8107 is 1

Step 1: Since 8107 > 2983, we apply the division lemma to 8107 and 2983, to get

8107 = 2983 x 2 + 2141

Step 2: Since the reminder 2983 ≠ 0, we apply division lemma to 2141 and 2983, to get

2983 = 2141 x 1 + 842

Step 3: We consider the new divisor 2141 and the new remainder 842, and apply the division lemma to get

2141 = 842 x 2 + 457

We consider the new divisor 842 and the new remainder 457,and apply the division lemma to get

842 = 457 x 1 + 385

We consider the new divisor 457 and the new remainder 385,and apply the division lemma to get

457 = 385 x 1 + 72

We consider the new divisor 385 and the new remainder 72,and apply the division lemma to get

385 = 72 x 5 + 25

We consider the new divisor 72 and the new remainder 25,and apply the division lemma to get

72 = 25 x 2 + 22

We consider the new divisor 25 and the new remainder 22,and apply the division lemma to get

25 = 22 x 1 + 3

We consider the new divisor 22 and the new remainder 3,and apply the division lemma to get

22 = 3 x 7 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2983 and 8107 is 1

Notice that 1 = HCF(3,1) = HCF(22,3) = HCF(25,22) = HCF(72,25) = HCF(385,72) = HCF(457,385) = HCF(842,457) = HCF(2141,842) = HCF(2983,2141) = HCF(8107,2983) .

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Frequently Asked Questions on HCF of 2983, 8107 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 2983, 8107?

Answer: HCF of 2983, 8107 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2983, 8107 using Euclid's Algorithm?

Answer: For arbitrary numbers 2983, 8107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.