Use our free GCF of Fractions Calculator tool to compute the GCF of 1/48, 57/378, 46/672 i.e 1/6048 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1/48, 57/378, 46/672.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 1/48,57/378,46/672
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 1/48,57/378,46/672, numerators are 1,57,46
Denominators are 48,378,672
The GCF of 1,57,46 is 1 .
LCM of 48,378,672 is 6048.
The greatest common factor of 1/48,57/378,46/672 = [GCF of 1,57,46]/[LCM of 48,378,672]= 1/6048
Therefore, the GCF of 1/48,57/378,46/672 is 1/6048.
To find the highest common factor of 1,57,46, we have to find the factors of both numbers and list the highest common factor.
The factors of 1 are 1
The factors of 57 are 1, 3, 19, 57
The factors of 46 are 1, 2, 23, 46
The HCF of 1,57,46 is 1.
Lets's calculate GCF of 1,57,46
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 1
:1
Now, list down the factors of 57
:1,3,19,57
Now, list down the factors of 46
:1,2,23,46
Greatest Common Factor
We found the factors 1,57,46 . The biggest common factor number is the GCF number.
So the greatest common factor 1,57,46 is 1.
Lets's calculate LCM of 48,378,672
2 | 48, 378, 672 |
2 | 24, 189, 336 |
2 | 12, 189, 168 |
2 | 6, 189, 84 |
3 | 3, 189, 42 |
7 | 1, 63, 14 |
1, 9, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 7 x 1 x 9 x 2 = 6048
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6048
Therefore, the GCF of Fractions 1/48,57/378,46/672 is 1/6048
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 48,378,672 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,378,672) = 6
common factors(in case of two or more numbers have common factors) = 336
GCF(48,378,672) x common factors =6 x 336 = 2016
LCM(48,378,672) = ( 48 × 378 × 672 ) / 2016
LCM(48,378,672) = 12192768 / 2016
LCM(48,378,672) = 6048
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 1,57,46?
The HCF of 1,57,46 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 1/48, 57/378, 46/672?
Answer: GCF of Numerators as per given numbers 1/48, 57/378, 46/672 is
GCF of Numerators i.e. for 1,57,46 is 1
LCM of denominators i.e. for 48,378,672 is 6048.
Thus, GCF of Fractions is 1/6048.Finally, GCF of Fractions for 1/48, 57/378, 46/672 is 1/6048.