Highest Common Factor of 5112, 6465 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 5112, 6465 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 5112, 6465 is 3 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 5112, 6465 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 5112, 6465 is 3.
HCF(5112, 6465) = 3
HCF of 5112, 6465 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5112, 6465 is 3.
Highest Common Factor of 5112,6465 is 3
Step 1: Since 6465 > 5112, we apply the division lemma to 6465 and 5112, to get
6465 = 5112 x 1 + 1353
Step 2: Since the reminder 5112 ≠ 0, we apply division lemma to 1353 and 5112, to get
5112 = 1353 x 3 + 1053
Step 3: We consider the new divisor 1353 and the new remainder 1053, and apply the division lemma to get
1353 = 1053 x 1 + 300
We consider the new divisor 1053 and the new remainder 300,and apply the division lemma to get
1053 = 300 x 3 + 153
We consider the new divisor 300 and the new remainder 153,and apply the division lemma to get
300 = 153 x 1 + 147
We consider the new divisor 153 and the new remainder 147,and apply the division lemma to get
153 = 147 x 1 + 6
We consider the new divisor 147 and the new remainder 6,and apply the division lemma to get
147 = 6 x 24 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 5112 and 6465 is 3
Notice that 3 = HCF(6,3) = HCF(147,6) = HCF(153,147) = HCF(300,153) = HCF(1053,300) = HCF(1353,1053) = HCF(5112,1353) = HCF(6465,5112) .
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Frequently Asked Questions on HCF of 5112, 6465 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 5112, 6465?
Answer: HCF of 5112, 6465 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5112, 6465 using Euclid's Algorithm?
Answer: For arbitrary numbers 5112, 6465 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.