Use our free GCF of Fractions Calculator tool to compute the GCF of 419/540, 740/784 i.e 1/105840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 419/540, 740/784.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 419/540,740/784
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 419/540,740/784, numerators are 419,740
Denominators are 540,784
The GCF of 419,740 is 1 .
LCM of 540,784 is 105840.
The greatest common factor of 419/540,740/784 = [GCF of 419,740]/[LCM of 540,784]= 1/105840
Therefore, the GCF of 419/540,740/784 is 1/105840.
To find the highest common factor of 419,740, we have to find the factors of both numbers and list the highest common factor.
The factors of 419 are 1, 419
The factors of 740 are 1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740
The HCF of 419,740 is 1.
Lets's calculate GCF of 419,740
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 419
:1,419
Now, list down the factors of 740
:1,2,4,5,10,20,37,74,148,185,370,740
Greatest Common Factor
We found the factors 419,740 . The biggest common factor number is the GCF number.
So the greatest common factor 419,740 is 1.
Lets's calculate LCM of 540,784
2 | 540, 784 |
2 | 270, 392 |
135, 196 |
∴ So the LCM of the given numbers is 2 x 2 x 135 x 196 = 105840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/105840
Therefore, the GCF of Fractions 419/540,740/784 is 1/105840
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 540,784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(540,784) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(540,784) x common factors =4 x 1 = 4
LCM(540,784) = ( 540 × 784 ) / 4
LCM(540,784) = 423360 / 4
LCM(540,784) = 105840
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 419,740?
The HCF of 419,740 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 419/540, 740/784?
Answer: GCF of Numerators as per given numbers 419/540, 740/784 is
GCF of Numerators i.e. for 419,740 is 1
LCM of denominators i.e. for 540,784 is 105840.
Thus, GCF of Fractions is 1/105840.Finally, GCF of Fractions for 419/540, 740/784 is 1/105840.