Use our free GCF of Fractions Calculator tool to compute the GCF of 126/394, 567/900 i.e 63/177300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 126/394, 567/900.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 126/394,567/900
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 126/394,567/900, numerators are 126,567
Denominators are 394,900
The GCF of 126,567 is 63 .
LCM of 394,900 is 177300.
The greatest common factor of 126/394,567/900 = [GCF of 126,567]/[LCM of 394,900]= 63/177300
Therefore, the GCF of 126/394,567/900 is 63/177300.
To find the highest common factor of 126,567, we have to find the factors of both numbers and list the highest common factor.
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567
The HCF of 126,567 is 63.
Lets's calculate GCF of 126,567
3 | 126, 567 |
3 | 42, 189 |
7 | 14, 63 |
2, 9 |
∴ So the GCF of the given numbers is 3 x 3 x 7 = 63
Now, list down the factors of 126
:1,2,3,6,7,9,14,18,21,42,63,126
Now, list down the factors of 567
:1,3,7,9,21,27,63,81,189,567
Greatest Common Factor
We found the factors 126,567 . The biggest common factor number is the GCF number.
So the greatest common factor 126,567 is 63.
Lets's calculate LCM of 394,900
2 | 394, 900 |
197, 450 |
∴ So the LCM of the given numbers is 2 x 197 x 450 = 177300
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 63/177300
Therefore, the GCF of Fractions 126/394,567/900 is 63/177300
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 394,900 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(394,900) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(394,900) x common factors =2 x 1 = 2
LCM(394,900) = ( 394 × 900 ) / 2
LCM(394,900) = 354600 / 2
LCM(394,900) = 177300
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 126,567?
The HCF of 126,567 is 63
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 126/394, 567/900?
Answer: GCF of Numerators as per given numbers 126/394, 567/900 is
GCF of Numerators i.e. for 126,567 is 63
LCM of denominators i.e. for 394,900 is 177300.
Thus, GCF of Fractions is 63/177300.Finally, GCF of Fractions for 126/394, 567/900 is 63/177300.