Highest Common Factor of 85, 204, 115 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 85, 204, 115 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 85, 204, 115 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 85, 204, 115 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 85, 204, 115 is 1.
HCF(85, 204, 115) = 1
HCF of 85, 204, 115 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 85, 204, 115 is 1.
Highest Common Factor of 85,204,115 is 1
Step 1: Since 204 > 85, we apply the division lemma to 204 and 85, to get
204 = 85 x 2 + 34
Step 2: Since the reminder 85 ≠ 0, we apply division lemma to 34 and 85, to get
85 = 34 x 2 + 17
Step 3: We consider the new divisor 34 and the new remainder 17, and apply the division lemma to get
34 = 17 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 85 and 204 is 17
Notice that 17 = HCF(34,17) = HCF(85,34) = HCF(204,85) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 115 > 17, we apply the division lemma to 115 and 17, to get
115 = 17 x 6 + 13
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 13 and 17, to get
17 = 13 x 1 + 4
Step 3: We consider the new divisor 13 and the new remainder 4, and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 17 and 115 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(115,17) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 85, 204, 115 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 85, 204, 115?
Answer: HCF of 85, 204, 115 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 85, 204, 115 using Euclid's Algorithm?
Answer: For arbitrary numbers 85, 204, 115 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.