Highest Common Factor of 415, 265, 430 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 415, 265, 430 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 415, 265, 430 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 415, 265, 430 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 415, 265, 430 is 5.
HCF(415, 265, 430) = 5
HCF of 415, 265, 430 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 415, 265, 430 is 5.
Highest Common Factor of 415,265,430 is 5
Step 1: Since 415 > 265, we apply the division lemma to 415 and 265, to get
415 = 265 x 1 + 150
Step 2: Since the reminder 265 ≠ 0, we apply division lemma to 150 and 265, to get
265 = 150 x 1 + 115
Step 3: We consider the new divisor 150 and the new remainder 115, and apply the division lemma to get
150 = 115 x 1 + 35
We consider the new divisor 115 and the new remainder 35,and apply the division lemma to get
115 = 35 x 3 + 10
We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get
35 = 10 x 3 + 5
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 415 and 265 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(115,35) = HCF(150,115) = HCF(265,150) = HCF(415,265) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 430 > 5, we apply the division lemma to 430 and 5, to get
430 = 5 x 86 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 430 is 5
Notice that 5 = HCF(430,5) .
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Frequently Asked Questions on HCF of 415, 265, 430 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 415, 265, 430?
Answer: HCF of 415, 265, 430 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 415, 265, 430 using Euclid's Algorithm?
Answer: For arbitrary numbers 415, 265, 430 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.