Use our free GCF of Fractions Calculator tool to compute the GCF of 749/780, 231/180 i.e 7/2340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 749/780, 231/180.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 749/780,231/180
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 749/780,231/180, numerators are 749,231
Denominators are 780,180
The GCF of 749,231 is 7 .
LCM of 780,180 is 2340.
The greatest common factor of 749/780,231/180 = [GCF of 749,231]/[LCM of 780,180]= 7/2340
Therefore, the GCF of 749/780,231/180 is 7/2340.
To find the highest common factor of 749,231, we have to find the factors of both numbers and list the highest common factor.
The factors of 749 are 1, 7, 107, 749
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The HCF of 749,231 is 7.
Lets's calculate GCF of 749,231
7 | 749, 231 |
107, 33 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 749
:1,7,107,749
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Greatest Common Factor
We found the factors 749,231 . The biggest common factor number is the GCF number.
So the greatest common factor 749,231 is 7.
Lets's calculate LCM of 780,180
2 | 780, 180 |
2 | 390, 90 |
3 | 195, 45 |
5 | 65, 15 |
13, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 13 x 3 = 2340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/2340
Therefore, the GCF of Fractions 749/780,231/180 is 7/2340
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 780,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(780,180) = 60
common factors(in case of two or more numbers have common factors) = 1
GCF(780,180) x common factors =60 x 1 = 60
LCM(780,180) = ( 780 × 180 ) / 60
LCM(780,180) = 140400 / 60
LCM(780,180) = 2340
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 749,231?
The HCF of 749,231 is 7
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 749/780, 231/180?
Answer: GCF of Numerators as per given numbers 749/780, 231/180 is
GCF of Numerators i.e. for 749,231 is 7
LCM of denominators i.e. for 780,180 is 2340.
Thus, GCF of Fractions is 7/2340.Finally, GCF of Fractions for 749/780, 231/180 is 7/2340.