Use our free GCF of Fractions Calculator tool to compute the GCF of 288/543, 144/406 i.e 144/220458 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/543, 144/406.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 288/543,144/406
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 288/543,144/406, numerators are 288,144
Denominators are 543,406
The GCF of 288,144 is 144 .
LCM of 543,406 is 220458.
The greatest common factor of 288/543,144/406 = [GCF of 288,144]/[LCM of 543,406]= 144/220458
Therefore, the GCF of 288/543,144/406 is 144/220458.
To find the highest common factor of 288,144, we have to find the factors of both numbers and list the highest common factor.
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The HCF of 288,144 is 144.
Lets's calculate GCF of 288,144
2 | 288, 144 |
2 | 144, 72 |
2 | 36, 72 |
2 | 18, 36 |
3 | 9, 18 |
3 | 3, 6 |
1, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 x 3 = 144
Now, list down the factors of 288
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288
Now, list down the factors of 144
:1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Greatest Common Factor
We found the factors 288,144 . The biggest common factor number is the GCF number.
So the greatest common factor 288,144 is 144.
Lets's calculate LCM of 543,406
Given numbers has no common factors except 1. So, there LCM is their product i.e 220458
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 144/220458
Therefore, the GCF of Fractions 288/543,144/406 is 144/220458
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 543,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(543,406) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(543,406) x common factors =1 x 1 = 1
LCM(543,406) = ( 543 × 406 ) / 1
LCM(543,406) = 220458 / 1
LCM(543,406) = 220458
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 288,144?
The HCF of 288,144 is 144
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 288/543, 144/406?
Answer: GCF of Numerators as per given numbers 288/543, 144/406 is
GCF of Numerators i.e. for 288,144 is 144
LCM of denominators i.e. for 543,406 is 220458.
Thus, GCF of Fractions is 144/220458.Finally, GCF of Fractions for 288/543, 144/406 is 144/220458.