Highest Common Factor of 2040, 747 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 2040, 747 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2040, 747 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 2040, 747 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 2040, 747 is 3.
HCF(2040, 747) = 3
HCF of 2040, 747 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2040, 747 is 3.
Highest Common Factor of 2040,747 is 3
Step 1: Since 2040 > 747, we apply the division lemma to 2040 and 747, to get
2040 = 747 x 2 + 546
Step 2: Since the reminder 747 ≠ 0, we apply division lemma to 546 and 747, to get
747 = 546 x 1 + 201
Step 3: We consider the new divisor 546 and the new remainder 201, and apply the division lemma to get
546 = 201 x 2 + 144
We consider the new divisor 201 and the new remainder 144,and apply the division lemma to get
201 = 144 x 1 + 57
We consider the new divisor 144 and the new remainder 57,and apply the division lemma to get
144 = 57 x 2 + 30
We consider the new divisor 57 and the new remainder 30,and apply the division lemma to get
57 = 30 x 1 + 27
We consider the new divisor 30 and the new remainder 27,and apply the division lemma to get
30 = 27 x 1 + 3
We consider the new divisor 27 and the new remainder 3,and apply the division lemma to get
27 = 3 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2040 and 747 is 3
Notice that 3 = HCF(27,3) = HCF(30,27) = HCF(57,30) = HCF(144,57) = HCF(201,144) = HCF(546,201) = HCF(747,546) = HCF(2040,747) .
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Frequently Asked Questions on HCF of 2040, 747 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 2040, 747?
Answer: HCF of 2040, 747 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2040, 747 using Euclid's Algorithm?
Answer: For arbitrary numbers 2040, 747 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.