Highest Common Factor of 516, 22612 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 516, 22612 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 22612 is 4 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 516, 22612 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 516, 22612 is 4.
HCF(516, 22612) = 4
HCF of 516, 22612 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 516, 22612 is 4.
Highest Common Factor of 516,22612 is 4
Step 1: Since 22612 > 516, we apply the division lemma to 22612 and 516, to get
22612 = 516 x 43 + 424
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 424 and 516, to get
516 = 424 x 1 + 92
Step 3: We consider the new divisor 424 and the new remainder 92, and apply the division lemma to get
424 = 92 x 4 + 56
We consider the new divisor 92 and the new remainder 56,and apply the division lemma to get
92 = 56 x 1 + 36
We consider the new divisor 56 and the new remainder 36,and apply the division lemma to get
56 = 36 x 1 + 20
We consider the new divisor 36 and the new remainder 20,and apply the division lemma to get
36 = 20 x 1 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 516 and 22612 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(36,20) = HCF(56,36) = HCF(92,56) = HCF(424,92) = HCF(516,424) = HCF(22612,516) .
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Frequently Asked Questions on HCF of 516, 22612 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 516, 22612?
Answer: HCF of 516, 22612 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 22612 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 22612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.