Use our free GCF of Fractions Calculator tool to compute the GCF of 252/723, 459/120 i.e 9/28920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 252/723, 459/120.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 252/723,459/120
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 252/723,459/120, numerators are 252,459
Denominators are 723,120
The GCF of 252,459 is 9 .
LCM of 723,120 is 28920.
The greatest common factor of 252/723,459/120 = [GCF of 252,459]/[LCM of 723,120]= 9/28920
Therefore, the GCF of 252/723,459/120 is 9/28920.
To find the highest common factor of 252,459, we have to find the factors of both numbers and list the highest common factor.
The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
The factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459
The HCF of 252,459 is 9.
Lets's calculate GCF of 252,459
3 | 252, 459 |
3 | 84, 153 |
28, 51 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 252
:1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252
Now, list down the factors of 459
:1,3,9,17,27,51,153,459
Greatest Common Factor
We found the factors 252,459 . The biggest common factor number is the GCF number.
So the greatest common factor 252,459 is 9.
Lets's calculate LCM of 723,120
3 | 723, 120 |
241, 40 |
∴ So the LCM of the given numbers is 3 x 241 x 40 = 28920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/28920
Therefore, the GCF of Fractions 252/723,459/120 is 9/28920
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 723,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(723,120) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(723,120) x common factors =3 x 1 = 3
LCM(723,120) = ( 723 × 120 ) / 3
LCM(723,120) = 86760 / 3
LCM(723,120) = 28920
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 252,459?
The HCF of 252,459 is 9
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 252/723, 459/120?
Answer: GCF of Numerators as per given numbers 252/723, 459/120 is
GCF of Numerators i.e. for 252,459 is 9
LCM of denominators i.e. for 723,120 is 28920.
Thus, GCF of Fractions is 9/28920.Finally, GCF of Fractions for 252/723, 459/120 is 9/28920.