Highest Common Factor of 380, 614, 915 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 380, 614, 915 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 380, 614, 915 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 380, 614, 915 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 380, 614, 915 is 1.

HCF(380, 614, 915) = 1

HCF of 380, 614, 915 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 380, 614, 915 is 1.

Highest Common Factor of 380,614,915 using Euclid's algorithm

Highest Common Factor of 380,614,915 is 1

Step 1: Since 614 > 380, we apply the division lemma to 614 and 380, to get

614 = 380 x 1 + 234

Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 234 and 380, to get

380 = 234 x 1 + 146

Step 3: We consider the new divisor 234 and the new remainder 146, and apply the division lemma to get

234 = 146 x 1 + 88

We consider the new divisor 146 and the new remainder 88,and apply the division lemma to get

146 = 88 x 1 + 58

We consider the new divisor 88 and the new remainder 58,and apply the division lemma to get

88 = 58 x 1 + 30

We consider the new divisor 58 and the new remainder 30,and apply the division lemma to get

58 = 30 x 1 + 28

We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get

30 = 28 x 1 + 2

We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get

28 = 2 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 380 and 614 is 2

Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(58,30) = HCF(88,58) = HCF(146,88) = HCF(234,146) = HCF(380,234) = HCF(614,380) .

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

Step 1: Since 915 > 2, we apply the division lemma to 915 and 2, to get

915 = 2 x 457 + 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 915 is 1

Notice that 1 = HCF(2,1) = HCF(915,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 380, 614, 915 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 380, 614, 915?

Answer: HCF of 380, 614, 915 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 380, 614, 915 using Euclid's Algorithm?

Answer: For arbitrary numbers 380, 614, 915 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.