Highest Common Factor of 6030, 5115 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 6030, 5115 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 6030, 5115 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 6030, 5115 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 6030, 5115 is 15.
HCF(6030, 5115) = 15
HCF of 6030, 5115 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6030, 5115 is 15.
Highest Common Factor of 6030,5115 is 15
Step 1: Since 6030 > 5115, we apply the division lemma to 6030 and 5115, to get
6030 = 5115 x 1 + 915
Step 2: Since the reminder 5115 ≠ 0, we apply division lemma to 915 and 5115, to get
5115 = 915 x 5 + 540
Step 3: We consider the new divisor 915 and the new remainder 540, and apply the division lemma to get
915 = 540 x 1 + 375
We consider the new divisor 540 and the new remainder 375,and apply the division lemma to get
540 = 375 x 1 + 165
We consider the new divisor 375 and the new remainder 165,and apply the division lemma to get
375 = 165 x 2 + 45
We consider the new divisor 165 and the new remainder 45,and apply the division lemma to get
165 = 45 x 3 + 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 6030 and 5115 is 15
Notice that 15 = HCF(30,15) = HCF(45,30) = HCF(165,45) = HCF(375,165) = HCF(540,375) = HCF(915,540) = HCF(5115,915) = HCF(6030,5115) .
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Frequently Asked Questions on HCF of 6030, 5115 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 6030, 5115?
Answer: HCF of 6030, 5115 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6030, 5115 using Euclid's Algorithm?
Answer: For arbitrary numbers 6030, 5115 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.