GCF of 540/42, 419/69, 254/23
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 540/42, 419/69, 254/23 i.e 1/966 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/42, 419/69, 254/23.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 540/42,419/69,254/23?
Given fractions are 540/42,419/69,254/23
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 540/42,419/69,254/23, numerators are 540,419,254
Denominators are 42,69,23
The GCF of 540,419,254 is 1 .
LCM of 42,69,23 is 966.
The greatest common factor of 540/42,419/69,254/23 = [GCF of 540,419,254]/[LCM of 42,69,23]= 1/966
Therefore, the GCF of 540/42,419/69,254/23 is 1/966.
To find the highest common factor of 540,419,254, we have to find the factors of both numbers and list the highest common factor.
The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The factors of 419 are 1, 419
The factors of 254 are 1, 2, 127, 254
The HCF of 540,419,254 is 1.
Lets's calculate GCF of 540,419,254
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 540,419,254 By Matching Biggest Common Factor Method
Now, list down the factors of 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Now, list down the factors of 419
:1,419
Now, list down the factors of 254
:1,2,127,254
Greatest Common Factor
We found the factors 540,419,254 . The biggest common factor number is the GCF number.
So the greatest common factor 540,419,254 is 1.
Lets's calculate LCM of 42,69,23
| 3 | 42, 69, 23 |
| 23 | 14, 23, 23 |
| 14, 1, 1 |
∴ So the LCM of the given numbers is 3 x 23 x 14 x 1 x 1 = 966
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/966
Therefore, the GCF of Fractions 540/42,419/69,254/23 is 1/966
Least Common Multiple of 42,69,23 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 42,69,23 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,69,23) = 1
common factors(in case of two or more numbers have common factors) = 69
GCF(42,69,23) x common factors =1 x 69 = 69
LCM(42,69,23) = ( 42 × 69 × 23 ) / 69
LCM(42,69,23) = 66654 / 69
LCM(42,69,23) = 966
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FAQs on GCF of Fractions of 540/42, 419/69, 254/23
1. What is the HCF of 540,419,254?
The HCF of 540,419,254 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 540/42, 419/69, 254/23?
Answer: GCF of Numerators as per given numbers 540/42, 419/69, 254/23 is
GCF of Numerators i.e. for 540,419,254 is 1
LCM of denominators i.e. for 42,69,23 is 966.
Thus, GCF of Fractions is 1/966.Finally, GCF of Fractions for 540/42, 419/69, 254/23 is 1/966.