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 5115, 1080 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 5115, 1080 is 15 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 5115, 1080 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 5115, 1080 is 15.
HCF(5115, 1080) = 15
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5115, 1080 is 15.
Step 1: Since 5115 > 1080, we apply the division lemma to 5115 and 1080, to get
5115 = 1080 x 4 + 795
Step 2: Since the reminder 1080 ≠ 0, we apply division lemma to 795 and 1080, to get
1080 = 795 x 1 + 285
Step 3: We consider the new divisor 795 and the new remainder 285, and apply the division lemma to get
795 = 285 x 2 + 225
We consider the new divisor 285 and the new remainder 225,and apply the division lemma to get
285 = 225 x 1 + 60
We consider the new divisor 225 and the new remainder 60,and apply the division lemma to get
225 = 60 x 3 + 45
We consider the new divisor 60 and the new remainder 45,and apply the division lemma to get
60 = 45 x 1 + 15
We consider the new divisor 45 and the new remainder 15,and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 5115 and 1080 is 15
Notice that 15 = HCF(45,15) = HCF(60,45) = HCF(225,60) = HCF(285,225) = HCF(795,285) = HCF(1080,795) = HCF(5115,1080) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 5115, 1080?
Answer: HCF of 5115, 1080 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5115, 1080 using Euclid's Algorithm?
Answer: For arbitrary numbers 5115, 1080 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.