Use our free GCF of Fractions Calculator tool to compute the GCF of 769/435, 574/219 i.e 1/31755 easily. The following is the detailed procedure to determine the greatest common factor of fractions 769/435, 574/219.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 769/435,574/219
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 769/435,574/219, numerators are 769,574
Denominators are 435,219
The GCF of 769,574 is 1 .
LCM of 435,219 is 31755.
The greatest common factor of 769/435,574/219 = [GCF of 769,574]/[LCM of 435,219]= 1/31755
Therefore, the GCF of 769/435,574/219 is 1/31755.
To find the highest common factor of 769,574, we have to find the factors of both numbers and list the highest common factor.
The factors of 769 are 1, 769
The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574
The HCF of 769,574 is 1.
Lets's calculate GCF of 769,574
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 769
:1,769
Now, list down the factors of 574
:1,2,7,14,41,82,287,574
Greatest Common Factor
We found the factors 769,574 . The biggest common factor number is the GCF number.
So the greatest common factor 769,574 is 1.
Lets's calculate LCM of 435,219
3 | 435, 219 |
145, 73 |
∴ So the LCM of the given numbers is 3 x 145 x 73 = 31755
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31755
Therefore, the GCF of Fractions 769/435,574/219 is 1/31755
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 435,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(435,219) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(435,219) x common factors =3 x 1 = 3
LCM(435,219) = ( 435 × 219 ) / 3
LCM(435,219) = 95265 / 3
LCM(435,219) = 31755
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 769,574?
The HCF of 769,574 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 769/435, 574/219?
Answer: GCF of Numerators as per given numbers 769/435, 574/219 is
GCF of Numerators i.e. for 769,574 is 1
LCM of denominators i.e. for 435,219 is 31755.
Thus, GCF of Fractions is 1/31755.Finally, GCF of Fractions for 769/435, 574/219 is 1/31755.