Highest Common Factor of 2255, 4105 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 2255, 4105 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 2255, 4105 is 5 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 2255, 4105 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 2255, 4105 is 5.
HCF(2255, 4105) = 5
HCF of 2255, 4105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2255, 4105 is 5.
Highest Common Factor of 2255,4105 is 5
Step 1: Since 4105 > 2255, we apply the division lemma to 4105 and 2255, to get
4105 = 2255 x 1 + 1850
Step 2: Since the reminder 2255 ≠ 0, we apply division lemma to 1850 and 2255, to get
2255 = 1850 x 1 + 405
Step 3: We consider the new divisor 1850 and the new remainder 405, and apply the division lemma to get
1850 = 405 x 4 + 230
We consider the new divisor 405 and the new remainder 230,and apply the division lemma to get
405 = 230 x 1 + 175
We consider the new divisor 230 and the new remainder 175,and apply the division lemma to get
230 = 175 x 1 + 55
We consider the new divisor 175 and the new remainder 55,and apply the division lemma to get
175 = 55 x 3 + 10
We consider the new divisor 55 and the new remainder 10,and apply the division lemma to get
55 = 10 x 5 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 2255 and 4105 is 5
Notice that 5 = HCF(10,5) = HCF(55,10) = HCF(175,55) = HCF(230,175) = HCF(405,230) = HCF(1850,405) = HCF(2255,1850) = HCF(4105,2255) .
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Frequently Asked Questions on HCF of 2255, 4105 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 2255, 4105?
Answer: HCF of 2255, 4105 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2255, 4105 using Euclid's Algorithm?
Answer: For arbitrary numbers 2255, 4105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.