Highest Common Factor of 6992, 8062 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 6992, 8062 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 6992, 8062 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 6992, 8062 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 6992, 8062 is 2.

HCF(6992, 8062) = 2

HCF of 6992, 8062 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 6992, 8062 is 2.

Highest Common Factor of 6992,8062 using Euclid's algorithm

Highest Common Factor of 6992,8062 is 2

Step 1: Since 8062 > 6992, we apply the division lemma to 8062 and 6992, to get

8062 = 6992 x 1 + 1070

Step 2: Since the reminder 6992 ≠ 0, we apply division lemma to 1070 and 6992, to get

6992 = 1070 x 6 + 572

Step 3: We consider the new divisor 1070 and the new remainder 572, and apply the division lemma to get

1070 = 572 x 1 + 498

We consider the new divisor 572 and the new remainder 498,and apply the division lemma to get

572 = 498 x 1 + 74

We consider the new divisor 498 and the new remainder 74,and apply the division lemma to get

498 = 74 x 6 + 54

We consider the new divisor 74 and the new remainder 54,and apply the division lemma to get

74 = 54 x 1 + 20

We consider the new divisor 54 and the new remainder 20,and apply the division lemma to get

54 = 20 x 2 + 14

We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get

20 = 14 x 1 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 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 6992 and 8062 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(54,20) = HCF(74,54) = HCF(498,74) = HCF(572,498) = HCF(1070,572) = HCF(6992,1070) = HCF(8062,6992) .

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Frequently Asked Questions on HCF of 6992, 8062 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 6992, 8062?

Answer: HCF of 6992, 8062 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6992, 8062 using Euclid's Algorithm?

Answer: For arbitrary numbers 6992, 8062 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.