Highest Common Factor of 2034, 263 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 2034, 263 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2034, 263 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 2034, 263 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 2034, 263 is 1.
HCF(2034, 263) = 1
HCF of 2034, 263 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2034, 263 is 1.
Highest Common Factor of 2034,263 is 1
Step 1: Since 2034 > 263, we apply the division lemma to 2034 and 263, to get
2034 = 263 x 7 + 193
Step 2: Since the reminder 263 ≠ 0, we apply division lemma to 193 and 263, to get
263 = 193 x 1 + 70
Step 3: We consider the new divisor 193 and the new remainder 70, and apply the division lemma to get
193 = 70 x 2 + 53
We consider the new divisor 70 and the new remainder 53,and apply the division lemma to get
70 = 53 x 1 + 17
We consider the new divisor 53 and the new remainder 17,and apply the division lemma to get
53 = 17 x 3 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 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 2034 and 263 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(53,17) = HCF(70,53) = HCF(193,70) = HCF(263,193) = HCF(2034,263) .
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Frequently Asked Questions on HCF of 2034, 263 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 2034, 263?
Answer: HCF of 2034, 263 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2034, 263 using Euclid's Algorithm?
Answer: For arbitrary numbers 2034, 263 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.