Highest Common Factor of 572, 2012 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 572, 2012 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 572, 2012 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 572, 2012 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 572, 2012 is 4.
HCF(572, 2012) = 4
HCF of 572, 2012 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 572, 2012 is 4.
Highest Common Factor of 572,2012 is 4
Step 1: Since 2012 > 572, we apply the division lemma to 2012 and 572, to get
2012 = 572 x 3 + 296
Step 2: Since the reminder 572 ≠ 0, we apply division lemma to 296 and 572, to get
572 = 296 x 1 + 276
Step 3: We consider the new divisor 296 and the new remainder 276, and apply the division lemma to get
296 = 276 x 1 + 20
We consider the new divisor 276 and the new remainder 20,and apply the division lemma to get
276 = 20 x 13 + 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 572 and 2012 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(276,20) = HCF(296,276) = HCF(572,296) = HCF(2012,572) .
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Frequently Asked Questions on HCF of 572, 2012 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 572, 2012?
Answer: HCF of 572, 2012 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 572, 2012 using Euclid's Algorithm?
Answer: For arbitrary numbers 572, 2012 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.