Highest Common Factor of 2158, 1254 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 2158, 1254 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2158, 1254 is 2 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 2158, 1254 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 2158, 1254 is 2.
HCF(2158, 1254) = 2
HCF of 2158, 1254 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2158, 1254 is 2.
Highest Common Factor of 2158,1254 is 2
Step 1: Since 2158 > 1254, we apply the division lemma to 2158 and 1254, to get
2158 = 1254 x 1 + 904
Step 2: Since the reminder 1254 ≠ 0, we apply division lemma to 904 and 1254, to get
1254 = 904 x 1 + 350
Step 3: We consider the new divisor 904 and the new remainder 350, and apply the division lemma to get
904 = 350 x 2 + 204
We consider the new divisor 350 and the new remainder 204,and apply the division lemma to get
350 = 204 x 1 + 146
We consider the new divisor 204 and the new remainder 146,and apply the division lemma to get
204 = 146 x 1 + 58
We consider the new divisor 146 and the new remainder 58,and apply the division lemma to get
146 = 58 x 2 + 30
We consider the new divisor 58 and the new remainder 30,and apply the division lemma to get
58 = 30 x 1 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2158 and 1254 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(58,30) = HCF(146,58) = HCF(204,146) = HCF(350,204) = HCF(904,350) = HCF(1254,904) = HCF(2158,1254) .
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Frequently Asked Questions on HCF of 2158, 1254 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 2158, 1254?
Answer: HCF of 2158, 1254 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2158, 1254 using Euclid's Algorithm?
Answer: For arbitrary numbers 2158, 1254 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.