Highest Common Factor of 406, 481, 113 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 406, 481, 113 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 406, 481, 113 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 406, 481, 113 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 406, 481, 113 is 1.
HCF(406, 481, 113) = 1
HCF of 406, 481, 113 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 406, 481, 113 is 1.
Highest Common Factor of 406,481,113 is 1
Step 1: Since 481 > 406, we apply the division lemma to 481 and 406, to get
481 = 406 x 1 + 75
Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 75 and 406, to get
406 = 75 x 5 + 31
Step 3: We consider the new divisor 75 and the new remainder 31, and apply the division lemma to get
75 = 31 x 2 + 13
We consider the new divisor 31 and the new remainder 13,and apply the division lemma to get
31 = 13 x 2 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 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 406 and 481 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(31,13) = HCF(75,31) = HCF(406,75) = HCF(481,406) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 113 > 1, we apply the division lemma to 113 and 1, to get
113 = 1 x 113 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 113 is 1
Notice that 1 = HCF(113,1) .
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Frequently Asked Questions on HCF of 406, 481, 113 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 406, 481, 113?
Answer: HCF of 406, 481, 113 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 406, 481, 113 using Euclid's Algorithm?
Answer: For arbitrary numbers 406, 481, 113 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
