Highest Common Factor of 5172, 6312 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 5172, 6312 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 5172, 6312 is 12 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 5172, 6312 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 5172, 6312 is 12.
HCF(5172, 6312) = 12
HCF of 5172, 6312 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5172, 6312 is 12.
Highest Common Factor of 5172,6312 is 12
Step 1: Since 6312 > 5172, we apply the division lemma to 6312 and 5172, to get
6312 = 5172 x 1 + 1140
Step 2: Since the reminder 5172 ≠ 0, we apply division lemma to 1140 and 5172, to get
5172 = 1140 x 4 + 612
Step 3: We consider the new divisor 1140 and the new remainder 612, and apply the division lemma to get
1140 = 612 x 1 + 528
We consider the new divisor 612 and the new remainder 528,and apply the division lemma to get
612 = 528 x 1 + 84
We consider the new divisor 528 and the new remainder 84,and apply the division lemma to get
528 = 84 x 6 + 24
We consider the new divisor 84 and the new remainder 24,and apply the division lemma to get
84 = 24 x 3 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 5172 and 6312 is 12
Notice that 12 = HCF(24,12) = HCF(84,24) = HCF(528,84) = HCF(612,528) = HCF(1140,612) = HCF(5172,1140) = HCF(6312,5172) .
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Frequently Asked Questions on HCF of 5172, 6312 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 5172, 6312?
Answer: HCF of 5172, 6312 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5172, 6312 using Euclid's Algorithm?
Answer: For arbitrary numbers 5172, 6312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.