Use our free GCF of Fractions Calculator tool to compute the GCF of 222/258, 108/540 i.e 6/23220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 222/258, 108/540.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 222/258,108/540
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 222/258,108/540, numerators are 222,108
Denominators are 258,540
The GCF of 222,108 is 6 .
LCM of 258,540 is 23220.
The greatest common factor of 222/258,108/540 = [GCF of 222,108]/[LCM of 258,540]= 6/23220
Therefore, the GCF of 222/258,108/540 is 6/23220.
To find the highest common factor of 222,108, we have to find the factors of both numbers and list the highest common factor.
The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The HCF of 222,108 is 6.
Lets's calculate GCF of 222,108
2 | 222, 108 |
3 | 111, 54 |
37, 18 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 222
:1,2,3,6,37,74,111,222
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Greatest Common Factor
We found the factors 222,108 . The biggest common factor number is the GCF number.
So the greatest common factor 222,108 is 6.
Lets's calculate LCM of 258,540
2 | 258, 540 |
3 | 129, 270 |
43, 90 |
∴ So the LCM of the given numbers is 2 x 3 x 43 x 90 = 23220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/23220
Therefore, the GCF of Fractions 222/258,108/540 is 6/23220
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 258,540 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(258,540) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(258,540) x common factors =6 x 1 = 6
LCM(258,540) = ( 258 × 540 ) / 6
LCM(258,540) = 139320 / 6
LCM(258,540) = 23220
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 222,108?
The HCF of 222,108 is 6
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 222/258, 108/540?
Answer: GCF of Numerators as per given numbers 222/258, 108/540 is
GCF of Numerators i.e. for 222,108 is 6
LCM of denominators i.e. for 258,540 is 23220.
Thus, GCF of Fractions is 6/23220.Finally, GCF of Fractions for 222/258, 108/540 is 6/23220.