Highest Common Factor of 205, 114, 228 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 205, 114, 228 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 205, 114, 228 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 205, 114, 228 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 205, 114, 228 is 1.
HCF(205, 114, 228) = 1
HCF of 205, 114, 228 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 205, 114, 228 is 1.
Highest Common Factor of 205,114,228 is 1
Step 1: Since 205 > 114, we apply the division lemma to 205 and 114, to get
205 = 114 x 1 + 91
Step 2: Since the reminder 114 ≠ 0, we apply division lemma to 91 and 114, to get
114 = 91 x 1 + 23
Step 3: We consider the new divisor 91 and the new remainder 23, and apply the division lemma to get
91 = 23 x 3 + 22
We consider the new divisor 23 and the new remainder 22,and apply the division lemma to get
23 = 22 x 1 + 1
We consider the new divisor 22 and the new remainder 1,and apply the division lemma to get
22 = 1 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 205 and 114 is 1
Notice that 1 = HCF(22,1) = HCF(23,22) = HCF(91,23) = HCF(114,91) = HCF(205,114) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 228 > 1, we apply the division lemma to 228 and 1, to get
228 = 1 x 228 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 228 is 1
Notice that 1 = HCF(228,1) .
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Frequently Asked Questions on HCF of 205, 114, 228 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 205, 114, 228?
Answer: HCF of 205, 114, 228 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 205, 114, 228 using Euclid's Algorithm?
Answer: For arbitrary numbers 205, 114, 228 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.