Highest Common Factor of 115, 412 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 115, 412 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 115, 412 is 1 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 115, 412 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 115, 412 is 1.
HCF(115, 412) = 1
HCF of 115, 412 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 115, 412 is 1.
Highest Common Factor of 115,412 is 1
Step 1: Since 412 > 115, we apply the division lemma to 412 and 115, to get
412 = 115 x 3 + 67
Step 2: Since the reminder 115 ≠ 0, we apply division lemma to 67 and 115, to get
115 = 67 x 1 + 48
Step 3: We consider the new divisor 67 and the new remainder 48, and apply the division lemma to get
67 = 48 x 1 + 19
We consider the new divisor 48 and the new remainder 19,and apply the division lemma to get
48 = 19 x 2 + 10
We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get
19 = 10 x 1 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 115 and 412 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(48,19) = HCF(67,48) = HCF(115,67) = HCF(412,115) .
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Frequently Asked Questions on HCF of 115, 412 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 115, 412?
Answer: HCF of 115, 412 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 115, 412 using Euclid's Algorithm?
Answer: For arbitrary numbers 115, 412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.