GCF of 364/54, 448/104
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 364/54, 448/104 i.e 28/2808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 364/54, 448/104.
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 364/54,448/104?
Given fractions are 364/54,448/104
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 364/54,448/104, numerators are 364,448
Denominators are 54,104
The GCF of 364,448 is 28 .
LCM of 54,104 is 2808.
The greatest common factor of 364/54,448/104 = [GCF of 364,448]/[LCM of 54,104]= 28/2808
Therefore, the GCF of 364/54,448/104 is 28/2808.
To find the highest common factor of 364,448, we have to find the factors of both numbers and list the highest common factor.
The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448
The HCF of 364,448 is 28.
Lets's calculate GCF of 364,448
| 2 | 364, 448 |
| 2 | 182, 224 |
| 7 | 91, 112 |
| 13, 16 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 364,448 By Matching Biggest Common Factor Method
Now, list down the factors of 364
:1,2,4,7,13,14,26,28,52,91,182,364
Now, list down the factors of 448
:1,2,4,7,8,14,16,28,32,56,64,112,224,448
Greatest Common Factor
We found the factors 364,448 . The biggest common factor number is the GCF number.
So the greatest common factor 364,448 is 28.
Lets's calculate LCM of 54,104
| 2 | 54, 104 |
| 27, 52 |
∴ So the LCM of the given numbers is 2 x 27 x 52 = 2808
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/2808
Therefore, the GCF of Fractions 364/54,448/104 is 28/2808
Least Common Multiple of 54,104 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 54,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,104) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,104) x common factors =2 x 1 = 2
LCM(54,104) = ( 54 × 104 ) / 2
LCM(54,104) = 5616 / 2
LCM(54,104) = 2808
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 364/54, 448/104
1. What is the HCF of 364,448?
The HCF of 364,448 is 28
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 364/54, 448/104?
Answer: GCF of Numerators as per given numbers 364/54, 448/104 is
GCF of Numerators i.e. for 364,448 is 28
LCM of denominators i.e. for 54,104 is 2808.
Thus, GCF of Fractions is 28/2808.Finally, GCF of Fractions for 364/54, 448/104 is 28/2808.