Highest Common Factor of 315, 9330, 5815 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, 9330, 5815 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 315, 9330, 5815 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 315, 9330, 5815 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, 9330, 5815 is 5.
HCF(315, 9330, 5815) = 5
HCF of 315, 9330, 5815 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, 9330, 5815 is 5.
Highest Common Factor of 315,9330,5815 is 5
Step 1: Since 9330 > 315, we apply the division lemma to 9330 and 315, to get
9330 = 315 x 29 + 195
Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 195 and 315, to get
315 = 195 x 1 + 120
Step 3: We consider the new divisor 195 and the new remainder 120, and apply the division lemma to get
195 = 120 x 1 + 75
We consider the new divisor 120 and the new remainder 75,and apply the division lemma to get
120 = 75 x 1 + 45
We consider the new divisor 75 and the new remainder 45,and apply the division lemma to get
75 = 45 x 1 + 30
We consider the new divisor 45 and the new remainder 30,and apply the division lemma to get
45 = 30 x 1 + 15
We consider the new divisor 30 and the new remainder 15,and apply the division lemma to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 315 and 9330 is 15
Notice that 15 = HCF(30,15) = HCF(45,30) = HCF(75,45) = HCF(120,75) = HCF(195,120) = HCF(315,195) = HCF(9330,315) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5815 > 15, we apply the division lemma to 5815 and 15, to get
5815 = 15 x 387 + 10
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 10 and 15, to get
15 = 10 x 1 + 5
Step 3: We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 15 and 5815 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(5815,15) .
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Frequently Asked Questions on HCF of 315, 9330, 5815 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, 9330, 5815?
Answer: HCF of 315, 9330, 5815 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 315, 9330, 5815 using Euclid's Algorithm?
Answer: For arbitrary numbers 315, 9330, 5815 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.