Highest Common Factor of 115, 66 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, 66 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 115, 66 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, 66 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, 66 is 1.
HCF(115, 66) = 1
HCF of 115, 66 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, 66 is 1.
Highest Common Factor of 115,66 is 1
Step 1: Since 115 > 66, we apply the division lemma to 115 and 66, to get
115 = 66 x 1 + 49
Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 49 and 66, to get
66 = 49 x 1 + 17
Step 3: We consider the new divisor 49 and the new remainder 17, and apply the division lemma to get
49 = 17 x 2 + 15
We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get
17 = 15 x 1 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 115 and 66 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(49,17) = HCF(66,49) = HCF(115,66) .
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Frequently Asked Questions on HCF of 115, 66 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, 66?
Answer: HCF of 115, 66 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 115, 66 using Euclid's Algorithm?
Answer: For arbitrary numbers 115, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.