Highest Common Factor of 543, 10128 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 543, 10128 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 543, 10128 is 3 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 543, 10128 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 543, 10128 is 3.
HCF(543, 10128) = 3
HCF of 543, 10128 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 543, 10128 is 3.
Highest Common Factor of 543,10128 is 3
Step 1: Since 10128 > 543, we apply the division lemma to 10128 and 543, to get
10128 = 543 x 18 + 354
Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 354 and 543, to get
543 = 354 x 1 + 189
Step 3: We consider the new divisor 354 and the new remainder 189, and apply the division lemma to get
354 = 189 x 1 + 165
We consider the new divisor 189 and the new remainder 165,and apply the division lemma to get
189 = 165 x 1 + 24
We consider the new divisor 165 and the new remainder 24,and apply the division lemma to get
165 = 24 x 6 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 543 and 10128 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(165,24) = HCF(189,165) = HCF(354,189) = HCF(543,354) = HCF(10128,543) .
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Frequently Asked Questions on HCF of 543, 10128 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 543, 10128?
Answer: HCF of 543, 10128 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 543, 10128 using Euclid's Algorithm?
Answer: For arbitrary numbers 543, 10128 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.