Use our free GCF of Fractions Calculator tool to compute the GCF of 75/48, 54/24, 21/561 i.e 3/8976 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/48, 54/24, 21/561.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/48,54/24,21/561
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 75/48,54/24,21/561, numerators are 75,54,21
Denominators are 48,24,561
The GCF of 75,54,21 is 3 .
LCM of 48,24,561 is 8976.
The greatest common factor of 75/48,54/24,21/561 = [GCF of 75,54,21]/[LCM of 48,24,561]= 3/8976
Therefore, the GCF of 75/48,54/24,21/561 is 3/8976.
To find the highest common factor of 75,54,21, we have to find the factors of both numbers and list the highest common factor.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 21 are 1, 3, 7, 21
The HCF of 75,54,21 is 3.
Lets's calculate GCF of 75,54,21
3 | 75, 54, 21 |
25, 18, 7 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 21
:1,3,7,21
Greatest Common Factor
We found the factors 75,54,21 . The biggest common factor number is the GCF number.
So the greatest common factor 75,54,21 is 3.
Lets's calculate LCM of 48,24,561
2 | 48, 24, 561 |
2 | 24, 12, 561 |
2 | 6, 12, 561 |
3 | 3, 6, 561 |
1, 2, 187 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 2 x 187 = 8976
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8976
Therefore, the GCF of Fractions 75/48,54/24,21/561 is 3/8976
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 48,24,561 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,24,561) = 3
common factors(in case of two or more numbers have common factors) = 24
GCF(48,24,561) x common factors =3 x 24 = 72
LCM(48,24,561) = ( 48 × 24 × 561 ) / 72
LCM(48,24,561) = 646272 / 72
LCM(48,24,561) = 8976
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 75,54,21?
The HCF of 75,54,21 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 75/48, 54/24, 21/561?
Answer: GCF of Numerators as per given numbers 75/48, 54/24, 21/561 is
GCF of Numerators i.e. for 75,54,21 is 3
LCM of denominators i.e. for 48,24,561 is 8976.
Thus, GCF of Fractions is 3/8976.Finally, GCF of Fractions for 75/48, 54/24, 21/561 is 3/8976.