Highest Common Factor of 7405, 8743, 76230 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 7405, 8743, 76230 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7405, 8743, 76230 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 7405, 8743, 76230 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 7405, 8743, 76230 is 1.

HCF(7405, 8743, 76230) = 1

HCF of 7405, 8743, 76230 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 7405, 8743, 76230 is 1.

Highest Common Factor of 7405,8743,76230 using Euclid's algorithm

Highest Common Factor of 7405,8743,76230 is 1

Step 1: Since 8743 > 7405, we apply the division lemma to 8743 and 7405, to get

8743 = 7405 x 1 + 1338

Step 2: Since the reminder 7405 ≠ 0, we apply division lemma to 1338 and 7405, to get

7405 = 1338 x 5 + 715

Step 3: We consider the new divisor 1338 and the new remainder 715, and apply the division lemma to get

1338 = 715 x 1 + 623

We consider the new divisor 715 and the new remainder 623,and apply the division lemma to get

715 = 623 x 1 + 92

We consider the new divisor 623 and the new remainder 92,and apply the division lemma to get

623 = 92 x 6 + 71

We consider the new divisor 92 and the new remainder 71,and apply the division lemma to get

92 = 71 x 1 + 21

We consider the new divisor 71 and the new remainder 21,and apply the division lemma to get

71 = 21 x 3 + 8

We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get

21 = 8 x 2 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 7405 and 8743 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(71,21) = HCF(92,71) = HCF(623,92) = HCF(715,623) = HCF(1338,715) = HCF(7405,1338) = HCF(8743,7405) .

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

Step 1: Since 76230 > 1, we apply the division lemma to 76230 and 1, to get

76230 = 1 x 76230 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 76230 is 1

Notice that 1 = HCF(76230,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 7405, 8743, 76230 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 7405, 8743, 76230?

Answer: HCF of 7405, 8743, 76230 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7405, 8743, 76230 using Euclid's Algorithm?

Answer: For arbitrary numbers 7405, 8743, 76230 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.