Use our free GCF of Fractions Calculator tool to compute the GCF of 234/108, 512/116 i.e 2/3132 easily. The following is the detailed procedure to determine the greatest common factor of fractions 234/108, 512/116.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 234/108,512/116
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 234/108,512/116, numerators are 234,512
Denominators are 108,116
The GCF of 234,512 is 2 .
LCM of 108,116 is 3132.
The greatest common factor of 234/108,512/116 = [GCF of 234,512]/[LCM of 108,116]= 2/3132
Therefore, the GCF of 234/108,512/116 is 2/3132.
To find the highest common factor of 234,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 234,512 is 2.
Lets's calculate GCF of 234,512
2 | 234, 512 |
117, 256 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 234
:1,2,3,6,9,13,18,26,39,78,117,234
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 234,512 . The biggest common factor number is the GCF number.
So the greatest common factor 234,512 is 2.
Lets's calculate LCM of 108,116
2 | 108, 116 |
2 | 54, 58 |
27, 29 |
∴ So the LCM of the given numbers is 2 x 2 x 27 x 29 = 3132
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3132
Therefore, the GCF of Fractions 234/108,512/116 is 2/3132
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 108,116 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(108,116) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(108,116) x common factors =4 x 1 = 4
LCM(108,116) = ( 108 × 116 ) / 4
LCM(108,116) = 12528 / 4
LCM(108,116) = 3132
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 234,512?
The HCF of 234,512 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 234/108, 512/116?
Answer: GCF of Numerators as per given numbers 234/108, 512/116 is
GCF of Numerators i.e. for 234,512 is 2
LCM of denominators i.e. for 108,116 is 3132.
Thus, GCF of Fractions is 2/3132.Finally, GCF of Fractions for 234/108, 512/116 is 2/3132.