Highest Common Factor of 381, 2892 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, 2892 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 381, 2892 is 3 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, 2892 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, 2892 is 3.
HCF(381, 2892) = 3
HCF of 381, 2892 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, 2892 is 3.
Highest Common Factor of 381,2892 is 3
Step 1: Since 2892 > 381, we apply the division lemma to 2892 and 381, to get
2892 = 381 x 7 + 225
Step 2: Since the reminder 381 ≠ 0, we apply division lemma to 225 and 381, to get
381 = 225 x 1 + 156
Step 3: We consider the new divisor 225 and the new remainder 156, and apply the division lemma to get
225 = 156 x 1 + 69
We consider the new divisor 156 and the new remainder 69,and apply the division lemma to get
156 = 69 x 2 + 18
We consider the new divisor 69 and the new remainder 18,and apply the division lemma to get
69 = 18 x 3 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 381 and 2892 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(69,18) = HCF(156,69) = HCF(225,156) = HCF(381,225) = HCF(2892,381) .
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Frequently Asked Questions on HCF of 381, 2892 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, 2892?
Answer: HCF of 381, 2892 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 381, 2892 using Euclid's Algorithm?
Answer: For arbitrary numbers 381, 2892 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.