Highest Common Factor of 543, 4674 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, 4674 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 543, 4674 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, 4674 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, 4674 is 3.
HCF(543, 4674) = 3
HCF of 543, 4674 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, 4674 is 3.
Highest Common Factor of 543,4674 is 3
Step 1: Since 4674 > 543, we apply the division lemma to 4674 and 543, to get
4674 = 543 x 8 + 330
Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 330 and 543, to get
543 = 330 x 1 + 213
Step 3: We consider the new divisor 330 and the new remainder 213, and apply the division lemma to get
330 = 213 x 1 + 117
We consider the new divisor 213 and the new remainder 117,and apply the division lemma to get
213 = 117 x 1 + 96
We consider the new divisor 117 and the new remainder 96,and apply the division lemma to get
117 = 96 x 1 + 21
We consider the new divisor 96 and the new remainder 21,and apply the division lemma to get
96 = 21 x 4 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 543 and 4674 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(96,21) = HCF(117,96) = HCF(213,117) = HCF(330,213) = HCF(543,330) = HCF(4674,543) .
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Frequently Asked Questions on HCF of 543, 4674 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, 4674?
Answer: HCF of 543, 4674 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 543, 4674 using Euclid's Algorithm?
Answer: For arbitrary numbers 543, 4674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.