Use our free GCF of Fractions Calculator tool to compute the GCF of 542/87, 502/69, 214/42 i.e 2/28014 easily. The following is the detailed procedure to determine the greatest common factor of fractions 542/87, 502/69, 214/42.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 542/87,502/69,214/42
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 542/87,502/69,214/42, numerators are 542,502,214
Denominators are 87,69,42
The GCF of 542,502,214 is 2 .
LCM of 87,69,42 is 28014.
The greatest common factor of 542/87,502/69,214/42 = [GCF of 542,502,214]/[LCM of 87,69,42]= 2/28014
Therefore, the GCF of 542/87,502/69,214/42 is 2/28014.
To find the highest common factor of 542,502,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 542 are 1, 2, 271, 542
The factors of 502 are 1, 2, 251, 502
The factors of 214 are 1, 2, 107, 214
The HCF of 542,502,214 is 2.
Lets's calculate GCF of 542,502,214
2 | 542, 502, 214 |
271, 251, 107 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 542
:1,2,271,542
Now, list down the factors of 502
:1,2,251,502
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 542,502,214 . The biggest common factor number is the GCF number.
So the greatest common factor 542,502,214 is 2.
Lets's calculate LCM of 87,69,42
3 | 87, 69, 42 |
29, 23, 14 |
∴ So the LCM of the given numbers is 3 x 29 x 23 x 14 = 28014
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/28014
Therefore, the GCF of Fractions 542/87,502/69,214/42 is 2/28014
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 87,69,42 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,69,42) = 3
common factors(in case of two or more numbers have common factors) = 3
GCF(87,69,42) x common factors =3 x 3 = 9
LCM(87,69,42) = ( 87 × 69 × 42 ) / 9
LCM(87,69,42) = 252126 / 9
LCM(87,69,42) = 28014
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 542,502,214?
The HCF of 542,502,214 is 2
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 542/87, 502/69, 214/42?
Answer: GCF of Numerators as per given numbers 542/87, 502/69, 214/42 is
GCF of Numerators i.e. for 542,502,214 is 2
LCM of denominators i.e. for 87,69,42 is 28014.
Thus, GCF of Fractions is 2/28014.Finally, GCF of Fractions for 542/87, 502/69, 214/42 is 2/28014.