Use our free GCF of Fractions Calculator tool to compute the GCF of 819/442, 630/977 i.e 63/431834 easily. The following is the detailed procedure to determine the greatest common factor of fractions 819/442, 630/977.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 819/442,630/977
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 819/442,630/977, numerators are 819,630
Denominators are 442,977
The GCF of 819,630 is 63 .
LCM of 442,977 is 431834.
The greatest common factor of 819/442,630/977 = [GCF of 819,630]/[LCM of 442,977]= 63/431834
Therefore, the GCF of 819/442,630/977 is 63/431834.
To find the highest common factor of 819,630, we have to find the factors of both numbers and list the highest common factor.
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
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 HCF of 819,630 is 63.
Lets's calculate GCF of 819,630
3 | 819, 630 |
3 | 273, 210 |
7 | 91, 70 |
13, 10 |
∴ So the GCF of the given numbers is 3 x 3 x 7 = 63
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
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
Greatest Common Factor
We found the factors 819,630 . The biggest common factor number is the GCF number.
So the greatest common factor 819,630 is 63.
Lets's calculate LCM of 442,977
Given numbers has no common factors except 1. So, there LCM is their product i.e 431834
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 63/431834
Therefore, the GCF of Fractions 819/442,630/977 is 63/431834
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 442,977 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(442,977) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(442,977) x common factors =1 x 1 = 1
LCM(442,977) = ( 442 × 977 ) / 1
LCM(442,977) = 431834 / 1
LCM(442,977) = 431834
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 819,630?
The HCF of 819,630 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 819/442, 630/977?
Answer: GCF of Numerators as per given numbers 819/442, 630/977 is
GCF of Numerators i.e. for 819,630 is 63
LCM of denominators i.e. for 442,977 is 431834.
Thus, GCF of Fractions is 63/431834.Finally, GCF of Fractions for 819/442, 630/977 is 63/431834.