Use our free GCF of Fractions Calculator tool to compute the GCF of 540/342, 283/322 i.e 1/55062 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/342, 283/322.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 540/342,283/322
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 540/342,283/322, numerators are 540,283
Denominators are 342,322
The GCF of 540,283 is 1 .
LCM of 342,322 is 55062.
The greatest common factor of 540/342,283/322 = [GCF of 540,283]/[LCM of 342,322]= 1/55062
Therefore, the GCF of 540/342,283/322 is 1/55062.
To find the highest common factor of 540,283, we have to find the factors of both numbers and list the highest common factor.
The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The factors of 283 are 1, 283
The HCF of 540,283 is 1.
Lets's calculate GCF of 540,283
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Now, list down the factors of 283
:1,283
Greatest Common Factor
We found the factors 540,283 . The biggest common factor number is the GCF number.
So the greatest common factor 540,283 is 1.
Lets's calculate LCM of 342,322
2 | 342, 322 |
171, 161 |
∴ So the LCM of the given numbers is 2 x 171 x 161 = 55062
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/55062
Therefore, the GCF of Fractions 540/342,283/322 is 1/55062
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 342,322 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,322) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(342,322) x common factors =2 x 1 = 2
LCM(342,322) = ( 342 × 322 ) / 2
LCM(342,322) = 110124 / 2
LCM(342,322) = 55062
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 540,283?
The HCF of 540,283 is 1
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 540/342, 283/322?
Answer: GCF of Numerators as per given numbers 540/342, 283/322 is
GCF of Numerators i.e. for 540,283 is 1
LCM of denominators i.e. for 342,322 is 55062.
Thus, GCF of Fractions is 1/55062.Finally, GCF of Fractions for 540/342, 283/322 is 1/55062.