Highest Common Factor of 381, 107 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 381, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 381, 107 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 381, 107 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 381, 107 is 1.

HCF(381, 107) = 1

HCF of 381, 107 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 381, 107 is 1.

Highest Common Factor of 381,107 using Euclid's algorithm

Highest Common Factor of 381,107 is 1

Step 1: Since 381 > 107, we apply the division lemma to 381 and 107, to get

381 = 107 x 3 + 60

Step 2: Since the reminder 107 ≠ 0, we apply division lemma to 60 and 107, to get

107 = 60 x 1 + 47

Step 3: We consider the new divisor 60 and the new remainder 47, and apply the division lemma to get

60 = 47 x 1 + 13

We consider the new divisor 47 and the new remainder 13,and apply the division lemma to get

47 = 13 x 3 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 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 381 and 107 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(47,13) = HCF(60,47) = HCF(107,60) = HCF(381,107) .

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Frequently Asked Questions on HCF of 381, 107 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 381, 107?

Answer: HCF of 381, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 381, 107 using Euclid's Algorithm?

Answer: For arbitrary numbers 381, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.