Highest Common Factor of 540, 2020 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 540, 2020 i.e. 20 the largest integer that leaves a remainder zero for all numbers.
HCF of 540, 2020 is 20 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 540, 2020 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 540, 2020 is 20.
HCF(540, 2020) = 20
HCF of 540, 2020 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 540, 2020 is 20.
Highest Common Factor of 540,2020 is 20
Step 1: Since 2020 > 540, we apply the division lemma to 2020 and 540, to get
2020 = 540 x 3 + 400
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 400 and 540, to get
540 = 400 x 1 + 140
Step 3: We consider the new divisor 400 and the new remainder 140, and apply the division lemma to get
400 = 140 x 2 + 120
We consider the new divisor 140 and the new remainder 120,and apply the division lemma to get
140 = 120 x 1 + 20
We consider the new divisor 120 and the new remainder 20,and apply the division lemma to get
120 = 20 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 540 and 2020 is 20
Notice that 20 = HCF(120,20) = HCF(140,120) = HCF(400,140) = HCF(540,400) = HCF(2020,540) .
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Frequently Asked Questions on HCF of 540, 2020 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 540, 2020?
Answer: HCF of 540, 2020 is 20 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 540, 2020 using Euclid's Algorithm?
Answer: For arbitrary numbers 540, 2020 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.