Highest Common Factor of 8000, 543 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 8000, 543 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8000, 543 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 8000, 543 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 8000, 543 is 1.
HCF(8000, 543) = 1
HCF of 8000, 543 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8000, 543 is 1.
Highest Common Factor of 8000,543 is 1
Step 1: Since 8000 > 543, we apply the division lemma to 8000 and 543, to get
8000 = 543 x 14 + 398
Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 398 and 543, to get
543 = 398 x 1 + 145
Step 3: We consider the new divisor 398 and the new remainder 145, and apply the division lemma to get
398 = 145 x 2 + 108
We consider the new divisor 145 and the new remainder 108,and apply the division lemma to get
145 = 108 x 1 + 37
We consider the new divisor 108 and the new remainder 37,and apply the division lemma to get
108 = 37 x 2 + 34
We consider the new divisor 37 and the new remainder 34,and apply the division lemma to get
37 = 34 x 1 + 3
We consider the new divisor 34 and the new remainder 3,and apply the division lemma to get
34 = 3 x 11 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8000 and 543 is 1
Notice that 1 = HCF(3,1) = HCF(34,3) = HCF(37,34) = HCF(108,37) = HCF(145,108) = HCF(398,145) = HCF(543,398) = HCF(8000,543) .
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Frequently Asked Questions on HCF of 8000, 543 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 8000, 543?
Answer: HCF of 8000, 543 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8000, 543 using Euclid's Algorithm?
Answer: For arbitrary numbers 8000, 543 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.