Use our free GCF of Fractions Calculator tool to compute the GCF of 642/768, 574/954 i.e 2/122112 easily. The following is the detailed procedure to determine the greatest common factor of fractions 642/768, 574/954.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 642/768,574/954
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 642/768,574/954, numerators are 642,574
Denominators are 768,954
The GCF of 642,574 is 2 .
LCM of 768,954 is 122112.
The greatest common factor of 642/768,574/954 = [GCF of 642,574]/[LCM of 768,954]= 2/122112
Therefore, the GCF of 642/768,574/954 is 2/122112.
To find the highest common factor of 642,574, we have to find the factors of both numbers and list the highest common factor.
The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642
The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574
The HCF of 642,574 is 2.
Lets's calculate GCF of 642,574
2 | 642, 574 |
321, 287 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 642
:1,2,3,6,107,214,321,642
Now, list down the factors of 574
:1,2,7,14,41,82,287,574
Greatest Common Factor
We found the factors 642,574 . The biggest common factor number is the GCF number.
So the greatest common factor 642,574 is 2.
Lets's calculate LCM of 768,954
2 | 768, 954 |
3 | 384, 477 |
128, 159 |
∴ So the LCM of the given numbers is 2 x 3 x 128 x 159 = 122112
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/122112
Therefore, the GCF of Fractions 642/768,574/954 is 2/122112
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 768,954 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(768,954) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(768,954) x common factors =6 x 1 = 6
LCM(768,954) = ( 768 × 954 ) / 6
LCM(768,954) = 732672 / 6
LCM(768,954) = 122112
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 642,574?
The HCF of 642,574 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 642/768, 574/954?
Answer: GCF of Numerators as per given numbers 642/768, 574/954 is
GCF of Numerators i.e. for 642,574 is 2
LCM of denominators i.e. for 768,954 is 122112.
Thus, GCF of Fractions is 2/122112.Finally, GCF of Fractions for 642/768, 574/954 is 2/122112.