Highest Common Factor of 315, 813 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 315, 813 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 315, 813 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 315, 813 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 315, 813 is 3.
HCF(315, 813) = 3
HCF of 315, 813 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 315, 813 is 3.
Highest Common Factor of 315,813 is 3
Step 1: Since 813 > 315, we apply the division lemma to 813 and 315, to get
813 = 315 x 2 + 183
Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 183 and 315, to get
315 = 183 x 1 + 132
Step 3: We consider the new divisor 183 and the new remainder 132, and apply the division lemma to get
183 = 132 x 1 + 51
We consider the new divisor 132 and the new remainder 51,and apply the division lemma to get
132 = 51 x 2 + 30
We consider the new divisor 51 and the new remainder 30,and apply the division lemma to get
51 = 30 x 1 + 21
We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get
30 = 21 x 1 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 315 and 813 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(51,30) = HCF(132,51) = HCF(183,132) = HCF(315,183) = HCF(813,315) .
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Frequently Asked Questions on HCF of 315, 813 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 315, 813?
Answer: HCF of 315, 813 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 315, 813 using Euclid's Algorithm?
Answer: For arbitrary numbers 315, 813 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.