Highest Common Factor of 381, 107, 300 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, 300 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 381, 107, 300 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, 300 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, 300 is 1.
HCF(381, 107, 300) = 1
HCF of 381, 107, 300 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 381, 107, 300 is 1.
Highest Common Factor of 381,107,300 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) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 300 > 1, we apply the division lemma to 300 and 1, to get
300 = 1 x 300 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 300 is 1
Notice that 1 = HCF(300,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 381, 107, 300 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, 300?
Answer: HCF of 381, 107, 300 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 381, 107, 300 using Euclid's Algorithm?
Answer: For arbitrary numbers 381, 107, 300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.