Highest Common Factor of 381, 672, 465 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, 672, 465 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 381, 672, 465 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, 672, 465 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, 672, 465 is 3.
HCF(381, 672, 465) = 3
HCF of 381, 672, 465 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, 672, 465 is 3.
Highest Common Factor of 381,672,465 is 3
Step 1: Since 672 > 381, we apply the division lemma to 672 and 381, to get
672 = 381 x 1 + 291
Step 2: Since the reminder 381 ≠ 0, we apply division lemma to 291 and 381, to get
381 = 291 x 1 + 90
Step 3: We consider the new divisor 291 and the new remainder 90, and apply the division lemma to get
291 = 90 x 3 + 21
We consider the new divisor 90 and the new remainder 21,and apply the division lemma to get
90 = 21 x 4 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 381 and 672 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(90,21) = HCF(291,90) = HCF(381,291) = HCF(672,381) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 465 > 3, we apply the division lemma to 465 and 3, to get
465 = 3 x 155 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 465 is 3
Notice that 3 = HCF(465,3) .
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Frequently Asked Questions on HCF of 381, 672, 465 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, 672, 465?
Answer: HCF of 381, 672, 465 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 381, 672, 465 using Euclid's Algorithm?
Answer: For arbitrary numbers 381, 672, 465 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.