Highest Common Factor of 380, 615 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 380, 615 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 380, 615 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 380, 615 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 380, 615 is 5.
HCF(380, 615) = 5
HCF of 380, 615 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 380, 615 is 5.
Highest Common Factor of 380,615 is 5
Step 1: Since 615 > 380, we apply the division lemma to 615 and 380, to get
615 = 380 x 1 + 235
Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 235 and 380, to get
380 = 235 x 1 + 145
Step 3: We consider the new divisor 235 and the new remainder 145, and apply the division lemma to get
235 = 145 x 1 + 90
We consider the new divisor 145 and the new remainder 90,and apply the division lemma to get
145 = 90 x 1 + 55
We consider the new divisor 90 and the new remainder 55,and apply the division lemma to get
90 = 55 x 1 + 35
We consider the new divisor 55 and the new remainder 35,and apply the division lemma to get
55 = 35 x 1 + 20
We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get
35 = 20 x 1 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 380 and 615 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(55,35) = HCF(90,55) = HCF(145,90) = HCF(235,145) = HCF(380,235) = HCF(615,380) .
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Frequently Asked Questions on HCF of 380, 615 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 380, 615?
Answer: HCF of 380, 615 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 380, 615 using Euclid's Algorithm?
Answer: For arbitrary numbers 380, 615 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.