Highest Common Factor of 2990, 8158 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 2990, 8158 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 2990, 8158 is 2 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 2990, 8158 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 2990, 8158 is 2.

HCF(2990, 8158) = 2

HCF of 2990, 8158 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 2990, 8158 is 2.

Highest Common Factor of 2990,8158 using Euclid's algorithm

Highest Common Factor of 2990,8158 is 2

Step 1: Since 8158 > 2990, we apply the division lemma to 8158 and 2990, to get

8158 = 2990 x 2 + 2178

Step 2: Since the reminder 2990 ≠ 0, we apply division lemma to 2178 and 2990, to get

2990 = 2178 x 1 + 812

Step 3: We consider the new divisor 2178 and the new remainder 812, and apply the division lemma to get

2178 = 812 x 2 + 554

We consider the new divisor 812 and the new remainder 554,and apply the division lemma to get

812 = 554 x 1 + 258

We consider the new divisor 554 and the new remainder 258,and apply the division lemma to get

554 = 258 x 2 + 38

We consider the new divisor 258 and the new remainder 38,and apply the division lemma to get

258 = 38 x 6 + 30

We consider the new divisor 38 and the new remainder 30,and apply the division lemma to get

38 = 30 x 1 + 8

We consider the new divisor 30 and the new remainder 8,and apply the division lemma to get

30 = 8 x 3 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2990 and 8158 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(38,30) = HCF(258,38) = HCF(554,258) = HCF(812,554) = HCF(2178,812) = HCF(2990,2178) = HCF(8158,2990) .

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Frequently Asked Questions on HCF of 2990, 8158 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 2990, 8158?

Answer: HCF of 2990, 8158 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2990, 8158 using Euclid's Algorithm?

Answer: For arbitrary numbers 2990, 8158 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.