Use our free GCF of Fractions Calculator tool to compute the GCF of 108/406, 927/312 i.e 9/63336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 108/406, 927/312.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 108/406,927/312
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 108/406,927/312, numerators are 108,927
Denominators are 406,312
The GCF of 108,927 is 9 .
LCM of 406,312 is 63336.
The greatest common factor of 108/406,927/312 = [GCF of 108,927]/[LCM of 406,312]= 9/63336
Therefore, the GCF of 108/406,927/312 is 9/63336.
To find the highest common factor of 108,927, we have to find the factors of both numbers and list the highest common factor.
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 927 are 1, 3, 9, 103, 309, 927
The HCF of 108,927 is 9.
Lets's calculate GCF of 108,927
3 | 108, 927 |
3 | 36, 309 |
12, 103 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Now, list down the factors of 927
:1,3,9,103,309,927
Greatest Common Factor
We found the factors 108,927 . The biggest common factor number is the GCF number.
So the greatest common factor 108,927 is 9.
Lets's calculate LCM of 406,312
2 | 406, 312 |
203, 156 |
∴ So the LCM of the given numbers is 2 x 203 x 156 = 63336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/63336
Therefore, the GCF of Fractions 108/406,927/312 is 9/63336
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 406,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,312) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(406,312) x common factors =2 x 1 = 2
LCM(406,312) = ( 406 × 312 ) / 2
LCM(406,312) = 126672 / 2
LCM(406,312) = 63336
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 108,927?
The HCF of 108,927 is 9
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 108/406, 927/312?
Answer: GCF of Numerators as per given numbers 108/406, 927/312 is
GCF of Numerators i.e. for 108,927 is 9
LCM of denominators i.e. for 406,312 is 63336.
Thus, GCF of Fractions is 9/63336.Finally, GCF of Fractions for 108/406, 927/312 is 9/63336.