Use our free GCF of Fractions Calculator tool to compute the GCF of 630/468, 126/610 i.e 126/142740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 630/468, 126/610.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 630/468,126/610
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 630/468,126/610, numerators are 630,126
Denominators are 468,610
The GCF of 630,126 is 126 .
LCM of 468,610 is 142740.
The greatest common factor of 630/468,126/610 = [GCF of 630,126]/[LCM of 468,610]= 126/142740
Therefore, the GCF of 630/468,126/610 is 126/142740.
To find the highest common factor of 630,126, we have to find the factors of both numbers and list the highest common factor.
The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
The HCF of 630,126 is 126.
Lets's calculate GCF of 630,126
2 | 630, 126 |
3 | 315, 63 |
3 | 105, 21 |
7 | 35, 7 |
5, 1 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 7 = 126
Now, list down the factors of 630
:1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630
Now, list down the factors of 126
:1,2,3,6,7,9,14,18,21,42,63,126
Greatest Common Factor
We found the factors 630,126 . The biggest common factor number is the GCF number.
So the greatest common factor 630,126 is 126.
Lets's calculate LCM of 468,610
2 | 468, 610 |
234, 305 |
∴ So the LCM of the given numbers is 2 x 234 x 305 = 142740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 126/142740
Therefore, the GCF of Fractions 630/468,126/610 is 126/142740
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 468,610 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(468,610) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(468,610) x common factors =2 x 1 = 2
LCM(468,610) = ( 468 × 610 ) / 2
LCM(468,610) = 285480 / 2
LCM(468,610) = 142740
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 630,126?
The HCF of 630,126 is 126
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 630/468, 126/610?
Answer: GCF of Numerators as per given numbers 630/468, 126/610 is
GCF of Numerators i.e. for 630,126 is 126
LCM of denominators i.e. for 468,610 is 142740.
Thus, GCF of Fractions is 126/142740.Finally, GCF of Fractions for 630/468, 126/610 is 126/142740.