Highest Common Factor of 543, 9712 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, 9712 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 543, 9712 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 543, 9712 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, 9712 is 1.
HCF(543, 9712) = 1
HCF of 543, 9712 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, 9712 is 1.
Highest Common Factor of 543,9712 is 1
Step 1: Since 9712 > 543, we apply the division lemma to 9712 and 543, to get
9712 = 543 x 17 + 481
Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 481 and 543, to get
543 = 481 x 1 + 62
Step 3: We consider the new divisor 481 and the new remainder 62, and apply the division lemma to get
481 = 62 x 7 + 47
We consider the new divisor 62 and the new remainder 47,and apply the division lemma to get
62 = 47 x 1 + 15
We consider the new divisor 47 and the new remainder 15,and apply the division lemma to get
47 = 15 x 3 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 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 543 and 9712 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(47,15) = HCF(62,47) = HCF(481,62) = HCF(543,481) = HCF(9712,543) .
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Frequently Asked Questions on HCF of 543, 9712 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, 9712?
Answer: HCF of 543, 9712 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 543, 9712 using Euclid's Algorithm?
Answer: For arbitrary numbers 543, 9712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.