GCF of 48/39, 96/24, 28/51, 31/78
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 48/39, 96/24, 28/51, 31/78 i.e 1/5304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 48/39, 96/24, 28/51, 31/78.
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 48/39,96/24,28/51,31/78?
Given fractions are 48/39,96/24,28/51,31/78
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 48/39,96/24,28/51,31/78, numerators are 48,96,28,31
Denominators are 39,24,51,78
The GCF of 48,96,28,31 is 1 .
LCM of 39,24,51,78 is 5304.
The greatest common factor of 48/39,96/24,28/51,31/78 = [GCF of 48,96,28,31]/[LCM of 39,24,51,78]= 1/5304
Therefore, the GCF of 48/39,96/24,28/51,31/78 is 1/5304.
To find the highest common factor of 48,96,28,31, we have to find the factors of both numbers and list the highest common factor.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 31 are 1, 31
The HCF of 48,96,28,31 is 1.
Lets's calculate GCF of 48,96,28,31
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 48,96,28,31 By Matching Biggest Common Factor Method
Now, list down the factors of 48
:1,2,3,4,6,8,12,16,24,48
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 31
:1,31
Greatest Common Factor
We found the factors 48,96,28,31 . The biggest common factor number is the GCF number.
So the greatest common factor 48,96,28,31 is 1.
Lets's calculate LCM of 39,24,51,78
| 2 | 39, 24, 51, 78 |
| 3 | 39, 12, 51, 39 |
| 13 | 13, 4, 17, 13 |
| 1, 4, 17, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 1 x 4 x 17 x 1 = 5304
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5304
Therefore, the GCF of Fractions 48/39,96/24,28/51,31/78 is 1/5304
Least Common Multiple of 39,24,51,78 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 39,24,51,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,24,51,78) = 3
common factors(in case of two or more numbers have common factors) = 234
GCF(39,24,51,78) x common factors =3 x 234 = 702
LCM(39,24,51,78) = ( 39 × 24 × 51 × 78 ) / 702
LCM(39,24,51,78) = 3723408 / 702
LCM(39,24,51,78) = 5304
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 48/39, 96/24, 28/51, 31/78
1. What is the HCF of 48,96,28,31?
The HCF of 48,96,28,31 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 48/39, 96/24, 28/51, 31/78?
Answer: GCF of Numerators as per given numbers 48/39, 96/24, 28/51, 31/78 is
GCF of Numerators i.e. for 48,96,28,31 is 1
LCM of denominators i.e. for 39,24,51,78 is 5304.
Thus, GCF of Fractions is 1/5304.Finally, GCF of Fractions for 48/39, 96/24, 28/51, 31/78 is 1/5304.