Use our free GCF of Fractions Calculator tool to compute the GCF of 60/86, 84/826, 180/590 i.e 12/177590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/86, 84/826, 180/590.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 60/86,84/826,180/590
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 60/86,84/826,180/590, numerators are 60,84,180
Denominators are 86,826,590
The GCF of 60,84,180 is 12 .
LCM of 86,826,590 is 177590.
The greatest common factor of 60/86,84/826,180/590 = [GCF of 60,84,180]/[LCM of 86,826,590]= 12/177590
Therefore, the GCF of 60/86,84/826,180/590 is 12/177590.
To find the highest common factor of 60,84,180, 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 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The HCF of 60,84,180 is 12.
Lets's calculate GCF of 60,84,180
2 | 60, 84, 180 |
2 | 30, 42, 90 |
3 | 15, 21, 45 |
5, 7, 15 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
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 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 180
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
Greatest Common Factor
We found the factors 60,84,180 . The biggest common factor number is the GCF number.
So the greatest common factor 60,84,180 is 12.
Lets's calculate LCM of 86,826,590
2 | 86, 826, 590 |
59 | 43, 413, 295 |
43, 7, 5 |
∴ So the LCM of the given numbers is 2 x 59 x 43 x 7 x 5 = 177590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/177590
Therefore, the GCF of Fractions 60/86,84/826,180/590 is 12/177590
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 86,826,590 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(86,826,590) = 2
common factors(in case of two or more numbers have common factors) = 118
GCF(86,826,590) x common factors =2 x 118 = 236
LCM(86,826,590) = ( 86 × 826 × 590 ) / 236
LCM(86,826,590) = 41911240 / 236
LCM(86,826,590) = 177590
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 60,84,180?
The HCF of 60,84,180 is 12
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 60/86, 84/826, 180/590?
Answer: GCF of Numerators as per given numbers 60/86, 84/826, 180/590 is
GCF of Numerators i.e. for 60,84,180 is 12
LCM of denominators i.e. for 86,826,590 is 177590.
Thus, GCF of Fractions is 12/177590.Finally, GCF of Fractions for 60/86, 84/826, 180/590 is 12/177590.