Use our free GCF of Fractions Calculator tool to compute the GCF of 520/219, 544/540 i.e 8/39420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 520/219, 544/540.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 520/219,544/540
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 520/219,544/540, numerators are 520,544
Denominators are 219,540
The GCF of 520,544 is 8 .
LCM of 219,540 is 39420.
The greatest common factor of 520/219,544/540 = [GCF of 520,544]/[LCM of 219,540]= 8/39420
Therefore, the GCF of 520/219,544/540 is 8/39420.
To find the highest common factor of 520,544, we have to find the factors of both numbers and list the highest common factor.
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
The factors of 544 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544
The HCF of 520,544 is 8.
Lets's calculate GCF of 520,544
2 | 520, 544 |
2 | 260, 272 |
2 | 130, 136 |
65, 68 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
Now, list down the factors of 544
:1,2,4,8,16,17,32,34,68,136,272,544
Greatest Common Factor
We found the factors 520,544 . The biggest common factor number is the GCF number.
So the greatest common factor 520,544 is 8.
Lets's calculate LCM of 219,540
3 | 219, 540 |
73, 180 |
∴ So the LCM of the given numbers is 3 x 73 x 180 = 39420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/39420
Therefore, the GCF of Fractions 520/219,544/540 is 8/39420
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 219,540 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,540) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(219,540) x common factors =3 x 1 = 3
LCM(219,540) = ( 219 × 540 ) / 3
LCM(219,540) = 118260 / 3
LCM(219,540) = 39420
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 520,544?
The HCF of 520,544 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 520/219, 544/540?
Answer: GCF of Numerators as per given numbers 520/219, 544/540 is
GCF of Numerators i.e. for 520,544 is 8
LCM of denominators i.e. for 219,540 is 39420.
Thus, GCF of Fractions is 8/39420.Finally, GCF of Fractions for 520/219, 544/540 is 8/39420.