Highest Common Factor of 228, 41905 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 228, 41905 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 228, 41905 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 228, 41905 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 228, 41905 is 1.
HCF(228, 41905) = 1
HCF of 228, 41905 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 228, 41905 is 1.
Highest Common Factor of 228,41905 is 1
Step 1: Since 41905 > 228, we apply the division lemma to 41905 and 228, to get
41905 = 228 x 183 + 181
Step 2: Since the reminder 228 ≠ 0, we apply division lemma to 181 and 228, to get
228 = 181 x 1 + 47
Step 3: We consider the new divisor 181 and the new remainder 47, and apply the division lemma to get
181 = 47 x 3 + 40
We consider the new divisor 47 and the new remainder 40,and apply the division lemma to get
47 = 40 x 1 + 7
We consider the new divisor 40 and the new remainder 7,and apply the division lemma to get
40 = 7 x 5 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 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 228 and 41905 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(40,7) = HCF(47,40) = HCF(181,47) = HCF(228,181) = HCF(41905,228) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 228, 41905 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 228, 41905?
Answer: HCF of 228, 41905 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 228, 41905 using Euclid's Algorithm?
Answer: For arbitrary numbers 228, 41905 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.