Use our free GCF of Fractions Calculator tool to compute the GCF of 62/18, 90/33, 31/33, 83/12 i.e 1/396 easily. The following is the detailed procedure to determine the greatest common factor of fractions 62/18, 90/33, 31/33, 83/12.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 62/18,90/33,31/33,83/12
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 62/18,90/33,31/33,83/12, numerators are 62,90,31,83
Denominators are 18,33,33,12
The GCF of 62,90,31,83 is 1 .
LCM of 18,33,33,12 is 396.
The greatest common factor of 62/18,90/33,31/33,83/12 = [GCF of 62,90,31,83]/[LCM of 18,33,33,12]= 1/396
Therefore, the GCF of 62/18,90/33,31/33,83/12 is 1/396.
To find the highest common factor of 62,90,31,83, we have to find the factors of both numbers and list the highest common factor.
The factors of 62 are 1, 2, 31, 62
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 31 are 1, 31
The factors of 83 are 1, 83
The HCF of 62,90,31,83 is 1.
Lets's calculate GCF of 62,90,31,83
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 62
:1,2,31,62
Now, list down the factors of 90
:1,2,3,5,6,9,10,15,18,30,45,90
Now, list down the factors of 31
:1,31
Now, list down the factors of 83
:1,83
Greatest Common Factor
We found the factors 62,90,31,83 . The biggest common factor number is the GCF number.
So the greatest common factor 62,90,31,83 is 1.
Lets's calculate LCM of 18,33,33,12
2 | 18, 33, 33, 12 |
3 | 9, 33, 33, 6 |
11 | 3, 11, 11, 2 |
3, 1, 1, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 11 x 3 x 1 x 1 x 2 = 396
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/396
Therefore, the GCF of Fractions 62/18,90/33,31/33,83/12 is 1/396
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 18,33,33,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,33,33,12) = 3
common factors(in case of two or more numbers have common factors) = 198
GCF(18,33,33,12) x common factors =3 x 198 = 594
LCM(18,33,33,12) = ( 18 × 33 × 33 × 12 ) / 594
LCM(18,33,33,12) = 235224 / 594
LCM(18,33,33,12) = 396
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 62,90,31,83?
The HCF of 62,90,31,83 is 1
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 62/18, 90/33, 31/33, 83/12?
Answer: GCF of Numerators as per given numbers 62/18, 90/33, 31/33, 83/12 is
GCF of Numerators i.e. for 62,90,31,83 is 1
LCM of denominators i.e. for 18,33,33,12 is 396.
Thus, GCF of Fractions is 1/396.Finally, GCF of Fractions for 62/18, 90/33, 31/33, 83/12 is 1/396.