GCF of 268/57, 146/48, 546/40
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 268/57, 146/48, 546/40 i.e 2/4560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 268/57, 146/48, 546/40.
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 268/57,146/48,546/40?
Given fractions are 268/57,146/48,546/40
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 268/57,146/48,546/40, numerators are 268,146,546
Denominators are 57,48,40
The GCF of 268,146,546 is 2 .
LCM of 57,48,40 is 4560.
The greatest common factor of 268/57,146/48,546/40 = [GCF of 268,146,546]/[LCM of 57,48,40]= 2/4560
Therefore, the GCF of 268/57,146/48,546/40 is 2/4560.
To find the highest common factor of 268,146,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 268 are 1, 2, 4, 67, 134, 268
The factors of 146 are 1, 2, 73, 146
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 268,146,546 is 2.
Lets's calculate GCF of 268,146,546
| 2 | 268, 146, 546 |
| 134, 73, 273 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 268,146,546 By Matching Biggest Common Factor Method
Now, list down the factors of 268
:1,2,4,67,134,268
Now, list down the factors of 146
:1,2,73,146
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 268,146,546 . The biggest common factor number is the GCF number.
So the greatest common factor 268,146,546 is 2.
Lets's calculate LCM of 57,48,40
| 2 | 57, 48, 40 |
| 2 | 57, 24, 20 |
| 2 | 57, 12, 10 |
| 3 | 57, 6, 5 |
| 19, 2, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 19 x 2 x 5 = 4560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4560
Therefore, the GCF of Fractions 268/57,146/48,546/40 is 2/4560
Least Common Multiple of 57,48,40 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 57,48,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,48,40) = 1
common factors(in case of two or more numbers have common factors) = 24
GCF(57,48,40) x common factors =1 x 24 = 24
LCM(57,48,40) = ( 57 × 48 × 40 ) / 24
LCM(57,48,40) = 109440 / 24
LCM(57,48,40) = 4560
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FAQs on GCF of Fractions of 268/57, 146/48, 546/40
1. What is the HCF of 268,146,546?
The HCF of 268,146,546 is 2
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 268/57, 146/48, 546/40?
Answer: GCF of Numerators as per given numbers 268/57, 146/48, 546/40 is
GCF of Numerators i.e. for 268,146,546 is 2
LCM of denominators i.e. for 57,48,40 is 4560.
Thus, GCF of Fractions is 2/4560.Finally, GCF of Fractions for 268/57, 146/48, 546/40 is 2/4560.