Highest Common Factor of 1643, 2703 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 1643, 2703 i.e. 53 the largest integer that leaves a remainder zero for all numbers.
HCF of 1643, 2703 is 53 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 1643, 2703 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 1643, 2703 is 53.
HCF(1643, 2703) = 53
HCF of 1643, 2703 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1643, 2703 is 53.
Highest Common Factor of 1643,2703 is 53
Step 1: Since 2703 > 1643, we apply the division lemma to 2703 and 1643, to get
2703 = 1643 x 1 + 1060
Step 2: Since the reminder 1643 ≠ 0, we apply division lemma to 1060 and 1643, to get
1643 = 1060 x 1 + 583
Step 3: We consider the new divisor 1060 and the new remainder 583, and apply the division lemma to get
1060 = 583 x 1 + 477
We consider the new divisor 583 and the new remainder 477,and apply the division lemma to get
583 = 477 x 1 + 106
We consider the new divisor 477 and the new remainder 106,and apply the division lemma to get
477 = 106 x 4 + 53
We consider the new divisor 106 and the new remainder 53,and apply the division lemma to get
106 = 53 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 53, the HCF of 1643 and 2703 is 53
Notice that 53 = HCF(106,53) = HCF(477,106) = HCF(583,477) = HCF(1060,583) = HCF(1643,1060) = HCF(2703,1643) .
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Frequently Asked Questions on HCF of 1643, 2703 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 1643, 2703?
Answer: HCF of 1643, 2703 is 53 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1643, 2703 using Euclid's Algorithm?
Answer: For arbitrary numbers 1643, 2703 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
