Highest Common Factor of 515, 315 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 515, 315 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 515, 315 is 5 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 515, 315 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 515, 315 is 5.
HCF(515, 315) = 5
HCF of 515, 315 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 515, 315 is 5.
Highest Common Factor of 515,315 is 5
Step 1: Since 515 > 315, we apply the division lemma to 515 and 315, to get
515 = 315 x 1 + 200
Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 200 and 315, to get
315 = 200 x 1 + 115
Step 3: We consider the new divisor 200 and the new remainder 115, and apply the division lemma to get
200 = 115 x 1 + 85
We consider the new divisor 115 and the new remainder 85,and apply the division lemma to get
115 = 85 x 1 + 30
We consider the new divisor 85 and the new remainder 30,and apply the division lemma to get
85 = 30 x 2 + 25
We consider the new divisor 30 and the new remainder 25,and apply the division lemma to get
30 = 25 x 1 + 5
We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 515 and 315 is 5
Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(85,30) = HCF(115,85) = HCF(200,115) = HCF(315,200) = HCF(515,315) .
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Frequently Asked Questions on HCF of 515, 315 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 515, 315?
Answer: HCF of 515, 315 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 515, 315 using Euclid's Algorithm?
Answer: For arbitrary numbers 515, 315 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.