Highest Common Factor of 415, 744, 130 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 415, 744, 130 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 415, 744, 130 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 415, 744, 130 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 415, 744, 130 is 1.

HCF(415, 744, 130) = 1

HCF of 415, 744, 130 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 415, 744, 130 is 1.

Highest Common Factor of 415,744,130 using Euclid's algorithm

Highest Common Factor of 415,744,130 is 1

Step 1: Since 744 > 415, we apply the division lemma to 744 and 415, to get

744 = 415 x 1 + 329

Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 329 and 415, to get

415 = 329 x 1 + 86

Step 3: We consider the new divisor 329 and the new remainder 86, and apply the division lemma to get

329 = 86 x 3 + 71

We consider the new divisor 86 and the new remainder 71,and apply the division lemma to get

86 = 71 x 1 + 15

We consider the new divisor 71 and the new remainder 15,and apply the division lemma to get

71 = 15 x 4 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 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 415 and 744 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(71,15) = HCF(86,71) = HCF(329,86) = HCF(415,329) = HCF(744,415) .

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

Step 1: Since 130 > 1, we apply the division lemma to 130 and 1, to get

130 = 1 x 130 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 130 is 1

Notice that 1 = HCF(130,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 415, 744, 130 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 415, 744, 130?

Answer: HCF of 415, 744, 130 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 415, 744, 130 using Euclid's Algorithm?

Answer: For arbitrary numbers 415, 744, 130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.