Highest Common Factor of 381, 648, 399 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, 648, 399 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 381, 648, 399 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, 648, 399 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, 648, 399 is 3.
HCF(381, 648, 399) = 3
HCF of 381, 648, 399 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, 648, 399 is 3.
Highest Common Factor of 381,648,399 is 3
Step 1: Since 648 > 381, we apply the division lemma to 648 and 381, to get
648 = 381 x 1 + 267
Step 2: Since the reminder 381 ≠ 0, we apply division lemma to 267 and 381, to get
381 = 267 x 1 + 114
Step 3: We consider the new divisor 267 and the new remainder 114, and apply the division lemma to get
267 = 114 x 2 + 39
We consider the new divisor 114 and the new remainder 39,and apply the division lemma to get
114 = 39 x 2 + 36
We consider the new divisor 39 and the new remainder 36,and apply the division lemma to get
39 = 36 x 1 + 3
We consider the new divisor 36 and the new remainder 3,and apply the division lemma to get
36 = 3 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 381 and 648 is 3
Notice that 3 = HCF(36,3) = HCF(39,36) = HCF(114,39) = HCF(267,114) = HCF(381,267) = HCF(648,381) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 399 > 3, we apply the division lemma to 399 and 3, to get
399 = 3 x 133 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 399 is 3
Notice that 3 = HCF(399,3) .
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, 648, 399 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, 648, 399?
Answer: HCF of 381, 648, 399 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 381, 648, 399 using Euclid's Algorithm?
Answer: For arbitrary numbers 381, 648, 399 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.