Use our free GCF of Fractions Calculator tool to compute the GCF of 802/204, 4584/516 i.e 2/8772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 802/204, 4584/516.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 802/204,4584/516
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 802/204,4584/516, numerators are 802,4584
Denominators are 204,516
The GCF of 802,4584 is 2 .
LCM of 204,516 is 8772.
The greatest common factor of 802/204,4584/516 = [GCF of 802,4584]/[LCM of 204,516]= 2/8772
Therefore, the GCF of 802/204,4584/516 is 2/8772.
To find the highest common factor of 802,4584, we have to find the factors of both numbers and list the highest common factor.
The factors of 802 are 1, 2, 401, 802
The factors of 4584 are 1, 2, 3, 4, 6, 8, 12, 24, 191, 382, 573, 764, 1146, 1528, 2292, 4584
The HCF of 802,4584 is 2.
Lets's calculate GCF of 802,4584
2 | 802, 4584 |
401, 2292 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 802
:1,2,401,802
Now, list down the factors of 4584
:1,2,3,4,6,8,12,24,191,382,573,764,1146,1528,2292,4584
Greatest Common Factor
We found the factors 802,4584 . The biggest common factor number is the GCF number.
So the greatest common factor 802,4584 is 2.
Lets's calculate LCM of 204,516
2 | 204, 516 |
2 | 102, 258 |
3 | 51, 129 |
17, 43 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 17 x 43 = 8772
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8772
Therefore, the GCF of Fractions 802/204,4584/516 is 2/8772
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 204,516 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(204,516) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(204,516) x common factors =12 x 1 = 12
LCM(204,516) = ( 204 × 516 ) / 12
LCM(204,516) = 105264 / 12
LCM(204,516) = 8772
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 802,4584?
The HCF of 802,4584 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 802/204, 4584/516?
Answer: GCF of Numerators as per given numbers 802/204, 4584/516 is
GCF of Numerators i.e. for 802,4584 is 2
LCM of denominators i.e. for 204,516 is 8772.
Thus, GCF of Fractions is 2/8772.Finally, GCF of Fractions for 802/204, 4584/516 is 2/8772.