Highest Common Factor of 7462, 8422, 76741 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 7462, 8422, 76741 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7462, 8422, 76741 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 7462, 8422, 76741 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 7462, 8422, 76741 is 1.

HCF(7462, 8422, 76741) = 1

HCF of 7462, 8422, 76741 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 7462, 8422, 76741 is 1.

Highest Common Factor of 7462,8422,76741 using Euclid's algorithm

Highest Common Factor of 7462,8422,76741 is 1

Step 1: Since 8422 > 7462, we apply the division lemma to 8422 and 7462, to get

8422 = 7462 x 1 + 960

Step 2: Since the reminder 7462 ≠ 0, we apply division lemma to 960 and 7462, to get

7462 = 960 x 7 + 742

Step 3: We consider the new divisor 960 and the new remainder 742, and apply the division lemma to get

960 = 742 x 1 + 218

We consider the new divisor 742 and the new remainder 218,and apply the division lemma to get

742 = 218 x 3 + 88

We consider the new divisor 218 and the new remainder 88,and apply the division lemma to get

218 = 88 x 2 + 42

We consider the new divisor 88 and the new remainder 42,and apply the division lemma to get

88 = 42 x 2 + 4

We consider the new divisor 42 and the new remainder 4,and apply the division lemma to get

42 = 4 x 10 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7462 and 8422 is 2

Notice that 2 = HCF(4,2) = HCF(42,4) = HCF(88,42) = HCF(218,88) = HCF(742,218) = HCF(960,742) = HCF(7462,960) = HCF(8422,7462) .

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

Step 1: Since 76741 > 2, we apply the division lemma to 76741 and 2, to get

76741 = 2 x 38370 + 1

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

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 76741 is 1

Notice that 1 = HCF(2,1) = HCF(76741,2) .

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Frequently Asked Questions on HCF of 7462, 8422, 76741 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 7462, 8422, 76741?

Answer: HCF of 7462, 8422, 76741 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7462, 8422, 76741 using Euclid's Algorithm?

Answer: For arbitrary numbers 7462, 8422, 76741 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.