Use our free GCF of Fractions Calculator tool to compute the GCF of 498/398, 972/984 i.e 6/195816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 498/398, 972/984.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 498/398,972/984
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 498/398,972/984, numerators are 498,972
Denominators are 398,984
The GCF of 498,972 is 6 .
LCM of 398,984 is 195816.
The greatest common factor of 498/398,972/984 = [GCF of 498,972]/[LCM of 398,984]= 6/195816
Therefore, the GCF of 498/398,972/984 is 6/195816.
To find the highest common factor of 498,972, 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 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The HCF of 498,972 is 6.
Lets's calculate GCF of 498,972
2 | 498, 972 |
3 | 249, 486 |
83, 162 |
∴ 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 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Greatest Common Factor
We found the factors 498,972 . The biggest common factor number is the GCF number.
So the greatest common factor 498,972 is 6.
Lets's calculate LCM of 398,984
2 | 398, 984 |
199, 492 |
∴ So the LCM of the given numbers is 2 x 199 x 492 = 195816
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/195816
Therefore, the GCF of Fractions 498/398,972/984 is 6/195816
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 398,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(398,984) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(398,984) x common factors =2 x 1 = 2
LCM(398,984) = ( 398 × 984 ) / 2
LCM(398,984) = 391632 / 2
LCM(398,984) = 195816
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 498,972?
The HCF of 498,972 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 498/398, 972/984?
Answer: GCF of Numerators as per given numbers 498/398, 972/984 is
GCF of Numerators i.e. for 498,972 is 6
LCM of denominators i.e. for 398,984 is 195816.
Thus, GCF of Fractions is 6/195816.Finally, GCF of Fractions for 498/398, 972/984 is 6/195816.