Highest Common Factor of 543, 665, 144 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, 665, 144 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 543, 665, 144 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, 665, 144 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, 665, 144 is 1.
HCF(543, 665, 144) = 1
HCF of 543, 665, 144 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, 665, 144 is 1.
Highest Common Factor of 543,665,144 is 1
Step 1: Since 665 > 543, we apply the division lemma to 665 and 543, to get
665 = 543 x 1 + 122
Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 122 and 543, to get
543 = 122 x 4 + 55
Step 3: We consider the new divisor 122 and the new remainder 55, and apply the division lemma to get
122 = 55 x 2 + 12
We consider the new divisor 55 and the new remainder 12,and apply the division lemma to get
55 = 12 x 4 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 665 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(55,12) = HCF(122,55) = HCF(543,122) = HCF(665,543) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 144 > 1, we apply the division lemma to 144 and 1, to get
144 = 1 x 144 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 144 is 1
Notice that 1 = HCF(144,1) .
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Frequently Asked Questions on HCF of 543, 665, 144 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, 665, 144?
Answer: HCF of 543, 665, 144 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 543, 665, 144 using Euclid's Algorithm?
Answer: For arbitrary numbers 543, 665, 144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.