Highest Common Factor of 118, 65 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 118, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 118, 65 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 118, 65 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 118, 65 is 1.
HCF(118, 65) = 1
HCF of 118, 65 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 118, 65 is 1.
Highest Common Factor of 118,65 is 1
Step 1: Since 118 > 65, we apply the division lemma to 118 and 65, to get
118 = 65 x 1 + 53
Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 53 and 65, to get
65 = 53 x 1 + 12
Step 3: We consider the new divisor 53 and the new remainder 12, and apply the division lemma to get
53 = 12 x 4 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 118 and 65 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(53,12) = HCF(65,53) = HCF(118,65) .
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Frequently Asked Questions on HCF of 118, 65 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 118, 65?
Answer: HCF of 118, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 118, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 118, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.