Use our free GCF of Fractions Calculator tool to compute the GCF of 152/390, 688/322 i.e 8/62790 easily. The following is the detailed procedure to determine the greatest common factor of fractions 152/390, 688/322.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 152/390,688/322
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 152/390,688/322, numerators are 152,688
Denominators are 390,322
The GCF of 152,688 is 8 .
LCM of 390,322 is 62790.
The greatest common factor of 152/390,688/322 = [GCF of 152,688]/[LCM of 390,322]= 8/62790
Therefore, the GCF of 152/390,688/322 is 8/62790.
To find the highest common factor of 152,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 152 are 1, 2, 4, 8, 19, 38, 76, 152
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 152,688 is 8.
Lets's calculate GCF of 152,688
2 | 152, 688 |
2 | 76, 344 |
2 | 38, 172 |
19, 86 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 152
:1,2,4,8,19,38,76,152
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 152,688 . The biggest common factor number is the GCF number.
So the greatest common factor 152,688 is 8.
Lets's calculate LCM of 390,322
2 | 390, 322 |
195, 161 |
∴ So the LCM of the given numbers is 2 x 195 x 161 = 62790
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/62790
Therefore, the GCF of Fractions 152/390,688/322 is 8/62790
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 390,322 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(390,322) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(390,322) x common factors =2 x 1 = 2
LCM(390,322) = ( 390 × 322 ) / 2
LCM(390,322) = 125580 / 2
LCM(390,322) = 62790
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 152,688?
The HCF of 152,688 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 152/390, 688/322?
Answer: GCF of Numerators as per given numbers 152/390, 688/322 is
GCF of Numerators i.e. for 152,688 is 8
LCM of denominators i.e. for 390,322 is 62790.
Thus, GCF of Fractions is 8/62790.Finally, GCF of Fractions for 152/390, 688/322 is 8/62790.