Highest Common Factor of 7345, 7976 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 7345, 7976 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7345, 7976 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 7345, 7976 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 7345, 7976 is 1.

HCF(7345, 7976) = 1

HCF of 7345, 7976 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 7345, 7976 is 1.

Highest Common Factor of 7345,7976 using Euclid's algorithm

Highest Common Factor of 7345,7976 is 1

Step 1: Since 7976 > 7345, we apply the division lemma to 7976 and 7345, to get

7976 = 7345 x 1 + 631

Step 2: Since the reminder 7345 ≠ 0, we apply division lemma to 631 and 7345, to get

7345 = 631 x 11 + 404

Step 3: We consider the new divisor 631 and the new remainder 404, and apply the division lemma to get

631 = 404 x 1 + 227

We consider the new divisor 404 and the new remainder 227,and apply the division lemma to get

404 = 227 x 1 + 177

We consider the new divisor 227 and the new remainder 177,and apply the division lemma to get

227 = 177 x 1 + 50

We consider the new divisor 177 and the new remainder 50,and apply the division lemma to get

177 = 50 x 3 + 27

We consider the new divisor 50 and the new remainder 27,and apply the division lemma to get

50 = 27 x 1 + 23

We consider the new divisor 27 and the new remainder 23,and apply the division lemma to get

27 = 23 x 1 + 4

We consider the new divisor 23 and the new remainder 4,and apply the division lemma to get

23 = 4 x 5 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 7345 and 7976 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(23,4) = HCF(27,23) = HCF(50,27) = HCF(177,50) = HCF(227,177) = HCF(404,227) = HCF(631,404) = HCF(7345,631) = HCF(7976,7345) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 7345, 7976 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 7345, 7976?

Answer: HCF of 7345, 7976 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7345, 7976 using Euclid's Algorithm?

Answer: For arbitrary numbers 7345, 7976 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.