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, 8300 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 381, 8300 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, 8300 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, 8300 is 1.
HCF(381, 8300) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 381, 8300 is 1.
Step 1: Since 8300 > 381, we apply the division lemma to 8300 and 381, to get
8300 = 381 x 21 + 299
Step 2: Since the reminder 381 ≠ 0, we apply division lemma to 299 and 381, to get
381 = 299 x 1 + 82
Step 3: We consider the new divisor 299 and the new remainder 82, and apply the division lemma to get
299 = 82 x 3 + 53
We consider the new divisor 82 and the new remainder 53,and apply the division lemma to get
82 = 53 x 1 + 29
We consider the new divisor 53 and the new remainder 29,and apply the division lemma to get
53 = 29 x 1 + 24
We consider the new divisor 29 and the new remainder 24,and apply the division lemma to get
29 = 24 x 1 + 5
We consider the new divisor 24 and the new remainder 5,and apply the division lemma to get
24 = 5 x 4 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 381 and 8300 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(24,5) = HCF(29,24) = HCF(53,29) = HCF(82,53) = HCF(299,82) = HCF(381,299) = HCF(8300,381) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 8300?
Answer: HCF of 381, 8300 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 381, 8300 using Euclid's Algorithm?
Answer: For arbitrary numbers 381, 8300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.