Use our free GCF of Fractions Calculator tool to compute the GCF of 168/748, 996/852 i.e 12/159324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/748, 996/852.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 168/748,996/852
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 168/748,996/852, numerators are 168,996
Denominators are 748,852
The GCF of 168,996 is 12 .
LCM of 748,852 is 159324.
The greatest common factor of 168/748,996/852 = [GCF of 168,996]/[LCM of 748,852]= 12/159324
Therefore, the GCF of 168/748,996/852 is 12/159324.
To find the highest common factor of 168,996, we have to find the factors of both numbers and list the highest common factor.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 996 are 1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, 996
The HCF of 168,996 is 12.
Lets's calculate GCF of 168,996
2 | 168, 996 |
2 | 84, 498 |
3 | 42, 249 |
14, 83 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Now, list down the factors of 996
:1,2,3,4,6,12,83,166,249,332,498,996
Greatest Common Factor
We found the factors 168,996 . The biggest common factor number is the GCF number.
So the greatest common factor 168,996 is 12.
Lets's calculate LCM of 748,852
2 | 748, 852 |
2 | 374, 426 |
187, 213 |
∴ So the LCM of the given numbers is 2 x 2 x 187 x 213 = 159324
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/159324
Therefore, the GCF of Fractions 168/748,996/852 is 12/159324
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 748,852 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(748,852) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(748,852) x common factors =4 x 1 = 4
LCM(748,852) = ( 748 × 852 ) / 4
LCM(748,852) = 637296 / 4
LCM(748,852) = 159324
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 168,996?
The HCF of 168,996 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 168/748, 996/852?
Answer: GCF of Numerators as per given numbers 168/748, 996/852 is
GCF of Numerators i.e. for 168,996 is 12
LCM of denominators i.e. for 748,852 is 159324.
Thus, GCF of Fractions is 12/159324.Finally, GCF of Fractions for 168/748, 996/852 is 12/159324.