Highest Common Factor of 402, 516, 461 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 402, 516, 461 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 402, 516, 461 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 402, 516, 461 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 402, 516, 461 is 1.
HCF(402, 516, 461) = 1
HCF of 402, 516, 461 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 402, 516, 461 is 1.
Highest Common Factor of 402,516,461 is 1
Step 1: Since 516 > 402, we apply the division lemma to 516 and 402, to get
516 = 402 x 1 + 114
Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 114 and 402, to get
402 = 114 x 3 + 60
Step 3: We consider the new divisor 114 and the new remainder 60, and apply the division lemma to get
114 = 60 x 1 + 54
We consider the new divisor 60 and the new remainder 54,and apply the division lemma to get
60 = 54 x 1 + 6
We consider the new divisor 54 and the new remainder 6,and apply the division lemma to get
54 = 6 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 402 and 516 is 6
Notice that 6 = HCF(54,6) = HCF(60,54) = HCF(114,60) = HCF(402,114) = HCF(516,402) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 461 > 6, we apply the division lemma to 461 and 6, to get
461 = 6 x 76 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 461 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(461,6) .
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Frequently Asked Questions on HCF of 402, 516, 461 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 402, 516, 461?
Answer: HCF of 402, 516, 461 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 402, 516, 461 using Euclid's Algorithm?
Answer: For arbitrary numbers 402, 516, 461 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
