Highest Common Factor of 2114, 2253 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 2114, 2253 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2114, 2253 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 2114, 2253 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 2114, 2253 is 1.
HCF(2114, 2253) = 1
HCF of 2114, 2253 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2114, 2253 is 1.
Highest Common Factor of 2114,2253 is 1
Step 1: Since 2253 > 2114, we apply the division lemma to 2253 and 2114, to get
2253 = 2114 x 1 + 139
Step 2: Since the reminder 2114 ≠ 0, we apply division lemma to 139 and 2114, to get
2114 = 139 x 15 + 29
Step 3: We consider the new divisor 139 and the new remainder 29, and apply the division lemma to get
139 = 29 x 4 + 23
We consider the new divisor 29 and the new remainder 23,and apply the division lemma to get
29 = 23 x 1 + 6
We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get
23 = 6 x 3 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2114 and 2253 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(29,23) = HCF(139,29) = HCF(2114,139) = HCF(2253,2114) .
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Frequently Asked Questions on HCF of 2114, 2253 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 2114, 2253?
Answer: HCF of 2114, 2253 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2114, 2253 using Euclid's Algorithm?
Answer: For arbitrary numbers 2114, 2253 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.