Highest Common Factor of 615, 380, 381 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 615, 380, 381 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 615, 380, 381 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 615, 380, 381 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 615, 380, 381 is 1.

HCF(615, 380, 381) = 1

HCF of 615, 380, 381 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 615, 380, 381 is 1.

Highest Common Factor of 615,380,381 using Euclid's algorithm

Highest Common Factor of 615,380,381 is 1

Step 1: Since 615 > 380, we apply the division lemma to 615 and 380, to get

615 = 380 x 1 + 235

Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 235 and 380, to get

380 = 235 x 1 + 145

Step 3: We consider the new divisor 235 and the new remainder 145, and apply the division lemma to get

235 = 145 x 1 + 90

We consider the new divisor 145 and the new remainder 90,and apply the division lemma to get

145 = 90 x 1 + 55

We consider the new divisor 90 and the new remainder 55,and apply the division lemma to get

90 = 55 x 1 + 35

We consider the new divisor 55 and the new remainder 35,and apply the division lemma to get

55 = 35 x 1 + 20

We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get

35 = 20 x 1 + 15

We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get

20 = 15 x 1 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 615 and 380 is 5

Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(55,35) = HCF(90,55) = HCF(145,90) = HCF(235,145) = HCF(380,235) = HCF(615,380) .

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

Step 1: Since 381 > 5, we apply the division lemma to 381 and 5, to get

381 = 5 x 76 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 381 is 1

Notice that 1 = HCF(5,1) = HCF(381,5) .

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Frequently Asked Questions on HCF of 615, 380, 381 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 615, 380, 381?

Answer: HCF of 615, 380, 381 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 615, 380, 381 using Euclid's Algorithm?

Answer: For arbitrary numbers 615, 380, 381 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.