Use our free GCF of Fractions Calculator tool to compute the GCF of 288/613, 912/216 i.e 48/132408 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/613, 912/216.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 288/613,912/216
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 288/613,912/216, numerators are 288,912
Denominators are 613,216
The GCF of 288,912 is 48 .
LCM of 613,216 is 132408.
The greatest common factor of 288/613,912/216 = [GCF of 288,912]/[LCM of 613,216]= 48/132408
Therefore, the GCF of 288/613,912/216 is 48/132408.
To find the highest common factor of 288,912, 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 912 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 912
The HCF of 288,912 is 48.
Lets's calculate GCF of 288,912
2 | 288, 912 |
2 | 144, 456 |
2 | 72, 228 |
2 | 36, 114 |
3 | 18, 57 |
6, 19 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 = 48
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 912
:1,2,3,4,6,8,12,16,19,24,38,48,57,76,114,152,228,304,456,912
Greatest Common Factor
We found the factors 288,912 . The biggest common factor number is the GCF number.
So the greatest common factor 288,912 is 48.
Lets's calculate LCM of 613,216
Given numbers has no common factors except 1. So, there LCM is their product i.e 132408
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 48/132408
Therefore, the GCF of Fractions 288/613,912/216 is 48/132408
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 613,216 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(613,216) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(613,216) x common factors =1 x 1 = 1
LCM(613,216) = ( 613 × 216 ) / 1
LCM(613,216) = 132408 / 1
LCM(613,216) = 132408
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 288,912?
The HCF of 288,912 is 48
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 288/613, 912/216?
Answer: GCF of Numerators as per given numbers 288/613, 912/216 is
GCF of Numerators i.e. for 288,912 is 48
LCM of denominators i.e. for 613,216 is 132408.
Thus, GCF of Fractions is 48/132408.Finally, GCF of Fractions for 288/613, 912/216 is 48/132408.