Use our free GCF of Fractions Calculator tool to compute the GCF of 69/75, 280/60, 292/144 i.e 1/3600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/75, 280/60, 292/144.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 69/75,280/60,292/144
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 69/75,280/60,292/144, numerators are 69,280,292
Denominators are 75,60,144
The GCF of 69,280,292 is 1 .
LCM of 75,60,144 is 3600.
The greatest common factor of 69/75,280/60,292/144 = [GCF of 69,280,292]/[LCM of 75,60,144]= 1/3600
Therefore, the GCF of 69/75,280/60,292/144 is 1/3600.
To find the highest common factor of 69,280,292, we have to find the factors of both numbers and list the highest common factor.
The factors of 69 are 1, 3, 23, 69
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The factors of 292 are 1, 2, 4, 73, 146, 292
The HCF of 69,280,292 is 1.
Lets's calculate GCF of 69,280,292
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Now, list down the factors of 292
:1,2,4,73,146,292
Greatest Common Factor
We found the factors 69,280,292 . The biggest common factor number is the GCF number.
So the greatest common factor 69,280,292 is 1.
Lets's calculate LCM of 75,60,144
2 | 75, 60, 144 |
2 | 75, 30, 72 |
3 | 75, 15, 36 |
5 | 25, 5, 12 |
1, 5, 12 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 5 x 12 = 3600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3600
Therefore, the GCF of Fractions 69/75,280/60,292/144 is 1/3600
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 75,60,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,60,144) = 3
common factors(in case of two or more numbers have common factors) = 60
GCF(75,60,144) x common factors =3 x 60 = 180
LCM(75,60,144) = ( 75 × 60 × 144 ) / 180
LCM(75,60,144) = 648000 / 180
LCM(75,60,144) = 3600
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 69,280,292?
The HCF of 69,280,292 is 1
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 69/75, 280/60, 292/144?
Answer: GCF of Numerators as per given numbers 69/75, 280/60, 292/144 is
GCF of Numerators i.e. for 69,280,292 is 1
LCM of denominators i.e. for 75,60,144 is 3600.
Thus, GCF of Fractions is 1/3600.Finally, GCF of Fractions for 69/75, 280/60, 292/144 is 1/3600.