Use our free GCF of Fractions Calculator tool to compute the GCF of 60/268, 46/166, 530/415 i.e 2/111220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/268, 46/166, 530/415.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 60/268,46/166,530/415
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 60/268,46/166,530/415, numerators are 60,46,530
Denominators are 268,166,415
The GCF of 60,46,530 is 2 .
LCM of 268,166,415 is 111220.
The greatest common factor of 60/268,46/166,530/415 = [GCF of 60,46,530]/[LCM of 268,166,415]= 2/111220
Therefore, the GCF of 60/268,46/166,530/415 is 2/111220.
To find the highest common factor of 60,46,530, we have to find the factors of both numbers and list the highest common factor.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 46 are 1, 2, 23, 46
The factors of 530 are 1, 2, 5, 10, 53, 106, 265, 530
The HCF of 60,46,530 is 2.
Lets's calculate GCF of 60,46,530
2 | 60, 46, 530 |
30, 23, 265 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 530
:1,2,5,10,53,106,265,530
Greatest Common Factor
We found the factors 60,46,530 . The biggest common factor number is the GCF number.
So the greatest common factor 60,46,530 is 2.
Lets's calculate LCM of 268,166,415
2 | 268, 166, 415 |
83 | 134, 83, 415 |
134, 1, 5 |
∴ So the LCM of the given numbers is 2 x 83 x 134 x 1 x 5 = 111220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/111220
Therefore, the GCF of Fractions 60/268,46/166,530/415 is 2/111220
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 268,166,415 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(268,166,415) = 1
common factors(in case of two or more numbers have common factors) = 166
GCF(268,166,415) x common factors =1 x 166 = 166
LCM(268,166,415) = ( 268 × 166 × 415 ) / 166
LCM(268,166,415) = 18462520 / 166
LCM(268,166,415) = 111220
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 60,46,530?
The HCF of 60,46,530 is 2
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 60/268, 46/166, 530/415?
Answer: GCF of Numerators as per given numbers 60/268, 46/166, 530/415 is
GCF of Numerators i.e. for 60,46,530 is 2
LCM of denominators i.e. for 268,166,415 is 111220.
Thus, GCF of Fractions is 2/111220.Finally, GCF of Fractions for 60/268, 46/166, 530/415 is 2/111220.