Use our free GCF of Fractions Calculator tool to compute the GCF of 42/90, 16/117, 649/753 i.e 1/293670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/90, 16/117, 649/753.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 42/90,16/117,649/753
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 42/90,16/117,649/753, numerators are 42,16,649
Denominators are 90,117,753
The GCF of 42,16,649 is 1 .
LCM of 90,117,753 is 293670.
The greatest common factor of 42/90,16/117,649/753 = [GCF of 42,16,649]/[LCM of 90,117,753]= 1/293670
Therefore, the GCF of 42/90,16/117,649/753 is 1/293670.
To find the highest common factor of 42,16,649, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 16 are 1, 2, 4, 8, 16
The factors of 649 are 1, 11, 59, 649
The HCF of 42,16,649 is 1.
Lets's calculate GCF of 42,16,649
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 16
:1,2,4,8,16
Now, list down the factors of 649
:1,11,59,649
Greatest Common Factor
We found the factors 42,16,649 . The biggest common factor number is the GCF number.
So the greatest common factor 42,16,649 is 1.
Lets's calculate LCM of 90,117,753
3 | 90, 117, 753 |
3 | 30, 39, 251 |
10, 13, 251 |
∴ So the LCM of the given numbers is 3 x 3 x 10 x 13 x 251 = 293670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/293670
Therefore, the GCF of Fractions 42/90,16/117,649/753 is 1/293670
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 90,117,753 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,117,753) = 3
common factors(in case of two or more numbers have common factors) = 9
GCF(90,117,753) x common factors =3 x 9 = 27
LCM(90,117,753) = ( 90 × 117 × 753 ) / 27
LCM(90,117,753) = 7929090 / 27
LCM(90,117,753) = 293670
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 42,16,649?
The HCF of 42,16,649 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 42/90, 16/117, 649/753?
Answer: GCF of Numerators as per given numbers 42/90, 16/117, 649/753 is
GCF of Numerators i.e. for 42,16,649 is 1
LCM of denominators i.e. for 90,117,753 is 293670.
Thus, GCF of Fractions is 1/293670.Finally, GCF of Fractions for 42/90, 16/117, 649/753 is 1/293670.