Use our free GCF of Fractions Calculator tool to compute the GCF of 72/68, 129/55, 288/550 i.e 3/18700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/68, 129/55, 288/550.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 72/68,129/55,288/550
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 72/68,129/55,288/550, numerators are 72,129,288
Denominators are 68,55,550
The GCF of 72,129,288 is 3 .
LCM of 68,55,550 is 18700.
The greatest common factor of 72/68,129/55,288/550 = [GCF of 72,129,288]/[LCM of 68,55,550]= 3/18700
Therefore, the GCF of 72/68,129/55,288/550 is 3/18700.
To find the highest common factor of 72,129,288, we have to find the factors of both numbers and list the highest common factor.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 129 are 1, 3, 43, 129
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The HCF of 72,129,288 is 3.
Lets's calculate GCF of 72,129,288
3 | 72, 129, 288 |
24, 43, 96 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 129
:1,3,43,129
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
Greatest Common Factor
We found the factors 72,129,288 . The biggest common factor number is the GCF number.
So the greatest common factor 72,129,288 is 3.
Lets's calculate LCM of 68,55,550
2 | 68, 55, 550 |
5 | 34, 55, 275 |
11 | 34, 11, 55 |
34, 1, 5 |
∴ So the LCM of the given numbers is 2 x 5 x 11 x 34 x 1 x 5 = 18700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/18700
Therefore, the GCF of Fractions 72/68,129/55,288/550 is 3/18700
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 68,55,550 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,55,550) = 1
common factors(in case of two or more numbers have common factors) = 110
GCF(68,55,550) x common factors =1 x 110 = 110
LCM(68,55,550) = ( 68 × 55 × 550 ) / 110
LCM(68,55,550) = 2057000 / 110
LCM(68,55,550) = 18700
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 72,129,288?
The HCF of 72,129,288 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 72/68, 129/55, 288/550?
Answer: GCF of Numerators as per given numbers 72/68, 129/55, 288/550 is
GCF of Numerators i.e. for 72,129,288 is 3
LCM of denominators i.e. for 68,55,550 is 18700.
Thus, GCF of Fractions is 3/18700.Finally, GCF of Fractions for 72/68, 129/55, 288/550 is 3/18700.