Use our free GCF of Fractions Calculator tool to compute the GCF of 784/727, 574/360 i.e 14/261720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/727, 574/360.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 784/727,574/360
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 784/727,574/360, numerators are 784,574
Denominators are 727,360
The GCF of 784,574 is 14 .
LCM of 727,360 is 261720.
The greatest common factor of 784/727,574/360 = [GCF of 784,574]/[LCM of 727,360]= 14/261720
Therefore, the GCF of 784/727,574/360 is 14/261720.
To find the highest common factor of 784,574, we have to find the factors of both numbers and list the highest common factor.
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574
The HCF of 784,574 is 14.
Lets's calculate GCF of 784,574
2 | 784, 574 |
7 | 392, 287 |
56, 41 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Now, list down the factors of 574
:1,2,7,14,41,82,287,574
Greatest Common Factor
We found the factors 784,574 . The biggest common factor number is the GCF number.
So the greatest common factor 784,574 is 14.
Lets's calculate LCM of 727,360
Given numbers has no common factors except 1. So, there LCM is their product i.e 261720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/261720
Therefore, the GCF of Fractions 784/727,574/360 is 14/261720
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 727,360 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(727,360) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(727,360) x common factors =1 x 1 = 1
LCM(727,360) = ( 727 × 360 ) / 1
LCM(727,360) = 261720 / 1
LCM(727,360) = 261720
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 784,574?
The HCF of 784,574 is 14
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 784/727, 574/360?
Answer: GCF of Numerators as per given numbers 784/727, 574/360 is
GCF of Numerators i.e. for 784,574 is 14
LCM of denominators i.e. for 727,360 is 261720.
Thus, GCF of Fractions is 14/261720.Finally, GCF of Fractions for 784/727, 574/360 is 14/261720.