Use our free GCF of Fractions Calculator tool to compute the GCF of 6872/120, 3168/7272 i.e 8/36360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6872/120, 3168/7272.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 6872/120,3168/7272
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 6872/120,3168/7272, numerators are 6872,3168
Denominators are 120,7272
The GCF of 6872,3168 is 8 .
LCM of 120,7272 is 36360.
The greatest common factor of 6872/120,3168/7272 = [GCF of 6872,3168]/[LCM of 120,7272]= 8/36360
Therefore, the GCF of 6872/120,3168/7272 is 8/36360.
To find the highest common factor of 6872,3168, we have to find the factors of both numbers and list the highest common factor.
The factors of 6872 are 1, 2, 4, 8, 859, 1718, 3436, 6872
The factors of 3168 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 32, 33, 36, 44, 48, 66, 72, 88, 96, 99, 132, 144, 176, 198, 264, 288, 352, 396, 528, 792, 1056, 1584, 3168
The HCF of 6872,3168 is 8.
Lets's calculate GCF of 6872,3168
2 | 6872, 3168 |
2 | 3436, 1584 |
2 | 1718, 792 |
859, 396 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 6872
:1,2,4,8,859,1718,3436,6872
Now, list down the factors of 3168
:1,2,3,4,6,8,9,11,12,16,18,22,24,32,33,36,44,48,66,72,88,96,99,132,144,176,198,264,288,352,396,528,792,1056,1584,3168
Greatest Common Factor
We found the factors 6872,3168 . The biggest common factor number is the GCF number.
So the greatest common factor 6872,3168 is 8.
Lets's calculate LCM of 120,7272
2 | 120, 7272 |
2 | 60, 3636 |
2 | 30, 1818 |
3 | 15, 909 |
5, 303 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 303 = 36360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/36360
Therefore, the GCF of Fractions 6872/120,3168/7272 is 8/36360
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 120,7272 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(120,7272) = 24
common factors(in case of two or more numbers have common factors) = 1
GCF(120,7272) x common factors =24 x 1 = 24
LCM(120,7272) = ( 120 × 7272 ) / 24
LCM(120,7272) = 872640 / 24
LCM(120,7272) = 36360
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 6872,3168?
The HCF of 6872,3168 is 8
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 6872/120, 3168/7272?
Answer: GCF of Numerators as per given numbers 6872/120, 3168/7272 is
GCF of Numerators i.e. for 6872,3168 is 8
LCM of denominators i.e. for 120,7272 is 36360.
Thus, GCF of Fractions is 8/36360.Finally, GCF of Fractions for 6872/120, 3168/7272 is 8/36360.