GCF of 4/84, 32/64, 48/557, 272/104
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4/84, 32/64, 48/557, 272/104 i.e 4/9731904 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4/84, 32/64, 48/557, 272/104.
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 4/84,32/64,48/557,272/104?
Given fractions are 4/84,32/64,48/557,272/104
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 4/84,32/64,48/557,272/104, numerators are 4,32,48,272
Denominators are 84,64,557,104
The GCF of 4,32,48,272 is 4 .
LCM of 84,64,557,104 is 9731904.
The greatest common factor of 4/84,32/64,48/557,272/104 = [GCF of 4,32,48,272]/[LCM of 84,64,557,104]= 4/9731904
Therefore, the GCF of 4/84,32/64,48/557,272/104 is 4/9731904.
To find the highest common factor of 4,32,48,272, we have to find the factors of both numbers and list the highest common factor.
The factors of 4 are 1, 2, 4
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272
The HCF of 4,32,48,272 is 4.
Lets's calculate GCF of 4,32,48,272
| 2 | 4, 32, 48, 272 |
| 2 | 2, 16, 24, 136 |
| 1, 8, 12, 68 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 4,32,48,272 By Matching Biggest Common Factor Method
Now, list down the factors of 4
:1,2,4
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 48
:1,2,3,4,6,8,12,16,24,48
Now, list down the factors of 272
:1,2,4,8,16,17,34,68,136,272
Greatest Common Factor
We found the factors 4,32,48,272 . The biggest common factor number is the GCF number.
So the greatest common factor 4,32,48,272 is 4.
Lets's calculate LCM of 84,64,557,104
| 2 | 84, 64, 557, 104 |
| 2 | 42, 32, 557, 52 |
| 2 | 21, 16, 557, 26 |
| 21, 8, 557, 13 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 21 x 8 x 557 x 13 = 9731904
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/9731904
Therefore, the GCF of Fractions 4/84,32/64,48/557,272/104 is 4/9731904
Least Common Multiple of 84,64,557,104 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 84,64,557,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,64,557,104) = 1
common factors(in case of two or more numbers have common factors) = 32
GCF(84,64,557,104) x common factors =1 x 32 = 32
LCM(84,64,557,104) = ( 84 × 64 × 557 × 104 ) / 32
LCM(84,64,557,104) = 311420928 / 32
LCM(84,64,557,104) = 9731904
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FAQs on GCF of Fractions of 4/84, 32/64, 48/557, 272/104
1. What is the HCF of 4,32,48,272?
The HCF of 4,32,48,272 is 4
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 4/84, 32/64, 48/557, 272/104?
Answer: GCF of Numerators as per given numbers 4/84, 32/64, 48/557, 272/104 is
GCF of Numerators i.e. for 4,32,48,272 is 4
LCM of denominators i.e. for 84,64,557,104 is 9731904.
Thus, GCF of Fractions is 4/9731904.Finally, GCF of Fractions for 4/84, 32/64, 48/557, 272/104 is 4/9731904.