Use our free GCF of Fractions Calculator tool to compute the GCF of 18/42, 13/57, 645/40 i.e 1/15960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 18/42, 13/57, 645/40.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 18/42,13/57,645/40
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 18/42,13/57,645/40, numerators are 18,13,645
Denominators are 42,57,40
The GCF of 18,13,645 is 1 .
LCM of 42,57,40 is 15960.
The greatest common factor of 18/42,13/57,645/40 = [GCF of 18,13,645]/[LCM of 42,57,40]= 1/15960
Therefore, the GCF of 18/42,13/57,645/40 is 1/15960.
To find the highest common factor of 18,13,645, we have to find the factors of both numbers and list the highest common factor.
The factors of 18 are 1, 2, 3, 6, 9, 18
The factors of 13 are 1, 13
The factors of 645 are 1, 3, 5, 15, 43, 129, 215, 645
The HCF of 18,13,645 is 1.
Lets's calculate GCF of 18,13,645
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 18
:1,2,3,6,9,18
Now, list down the factors of 13
:1,13
Now, list down the factors of 645
:1,3,5,15,43,129,215,645
Greatest Common Factor
We found the factors 18,13,645 . The biggest common factor number is the GCF number.
So the greatest common factor 18,13,645 is 1.
Lets's calculate LCM of 42,57,40
2 | 42, 57, 40 |
3 | 21, 57, 20 |
7, 19, 20 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 19 x 20 = 15960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15960
Therefore, the GCF of Fractions 18/42,13/57,645/40 is 1/15960
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 42,57,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,57,40) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(42,57,40) x common factors =1 x 6 = 6
LCM(42,57,40) = ( 42 × 57 × 40 ) / 6
LCM(42,57,40) = 95760 / 6
LCM(42,57,40) = 15960
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 18,13,645?
The HCF of 18,13,645 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 18/42, 13/57, 645/40?
Answer: GCF of Numerators as per given numbers 18/42, 13/57, 645/40 is
GCF of Numerators i.e. for 18,13,645 is 1
LCM of denominators i.e. for 42,57,40 is 15960.
Thus, GCF of Fractions is 1/15960.Finally, GCF of Fractions for 18/42, 13/57, 645/40 is 1/15960.