GCF of 48/78, 54/83, 75/318
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 48/78, 54/83, 75/318 i.e 3/343122 easily. The following is the detailed procedure to determine the greatest common factor of fractions 48/78, 54/83, 75/318.
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 48/78,54/83,75/318?
Given fractions are 48/78,54/83,75/318
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 48/78,54/83,75/318, numerators are 48,54,75
Denominators are 78,83,318
The GCF of 48,54,75 is 3 .
LCM of 78,83,318 is 343122.
The greatest common factor of 48/78,54/83,75/318 = [GCF of 48,54,75]/[LCM of 78,83,318]= 3/343122
Therefore, the GCF of 48/78,54/83,75/318 is 3/343122.
To find the highest common factor of 48,54,75, 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 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 75 are 1, 3, 5, 15, 25, 75
The HCF of 48,54,75 is 3.
Lets's calculate GCF of 48,54,75
| 3 | 48, 54, 75 |
| 16, 18, 25 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 48,54,75 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 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 75
:1,3,5,15,25,75
Greatest Common Factor
We found the factors 48,54,75 . The biggest common factor number is the GCF number.
So the greatest common factor 48,54,75 is 3.
Lets's calculate LCM of 78,83,318
| 2 | 78, 83, 318 |
| 3 | 39, 83, 159 |
| 13, 83, 53 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 83 x 53 = 343122
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/343122
Therefore, the GCF of Fractions 48/78,54/83,75/318 is 3/343122
Least Common Multiple of 78,83,318 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 78,83,318 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,83,318) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(78,83,318) x common factors =1 x 6 = 6
LCM(78,83,318) = ( 78 × 83 × 318 ) / 6
LCM(78,83,318) = 2058732 / 6
LCM(78,83,318) = 343122
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FAQs on GCF of Fractions of 48/78, 54/83, 75/318
1. What is the HCF of 48,54,75?
The HCF of 48,54,75 is 3
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 48/78, 54/83, 75/318?
Answer: GCF of Numerators as per given numbers 48/78, 54/83, 75/318 is
GCF of Numerators i.e. for 48,54,75 is 3
LCM of denominators i.e. for 78,83,318 is 343122.
Thus, GCF of Fractions is 3/343122.Finally, GCF of Fractions for 48/78, 54/83, 75/318 is 3/343122.