Use our free GCF of Fractions Calculator tool to compute the GCF of 498/234, 420/880 i.e 6/102960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 498/234, 420/880.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 498/234,420/880
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 498/234,420/880, numerators are 498,420
Denominators are 234,880
The GCF of 498,420 is 6 .
LCM of 234,880 is 102960.
The greatest common factor of 498/234,420/880 = [GCF of 498,420]/[LCM of 234,880]= 6/102960
Therefore, the GCF of 498/234,420/880 is 6/102960.
To find the highest common factor of 498,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 498 are 1, 2, 3, 6, 83, 166, 249, 498
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 498,420 is 6.
Lets's calculate GCF of 498,420
2 | 498, 420 |
3 | 249, 210 |
83, 70 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 498
:1,2,3,6,83,166,249,498
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 498,420 . The biggest common factor number is the GCF number.
So the greatest common factor 498,420 is 6.
Lets's calculate LCM of 234,880
2 | 234, 880 |
117, 440 |
∴ So the LCM of the given numbers is 2 x 117 x 440 = 102960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/102960
Therefore, the GCF of Fractions 498/234,420/880 is 6/102960
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 234,880 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(234,880) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(234,880) x common factors =2 x 1 = 2
LCM(234,880) = ( 234 × 880 ) / 2
LCM(234,880) = 205920 / 2
LCM(234,880) = 102960
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 498,420?
The HCF of 498,420 is 6
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 498/234, 420/880?
Answer: GCF of Numerators as per given numbers 498/234, 420/880 is
GCF of Numerators i.e. for 498,420 is 6
LCM of denominators i.e. for 234,880 is 102960.
Thus, GCF of Fractions is 6/102960.Finally, GCF of Fractions for 498/234, 420/880 is 6/102960.