Use our free GCF of Fractions Calculator tool to compute the GCF of 35/40, 58/57, 55/120 i.e 1/2280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/40, 58/57, 55/120.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 35/40,58/57,55/120
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 35/40,58/57,55/120, numerators are 35,58,55
Denominators are 40,57,120
The GCF of 35,58,55 is 1 .
LCM of 40,57,120 is 2280.
The greatest common factor of 35/40,58/57,55/120 = [GCF of 35,58,55]/[LCM of 40,57,120]= 1/2280
Therefore, the GCF of 35/40,58/57,55/120 is 1/2280.
To find the highest common factor of 35,58,55, we have to find the factors of both numbers and list the highest common factor.
The factors of 35 are 1, 5, 7, 35
The factors of 58 are 1, 2, 29, 58
The factors of 55 are 1, 5, 11, 55
The HCF of 35,58,55 is 1.
Lets's calculate GCF of 35,58,55
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 58
:1,2,29,58
Now, list down the factors of 55
:1,5,11,55
Greatest Common Factor
We found the factors 35,58,55 . The biggest common factor number is the GCF number.
So the greatest common factor 35,58,55 is 1.
Lets's calculate LCM of 40,57,120
2 | 40, 57, 120 |
2 | 20, 57, 60 |
2 | 10, 57, 30 |
3 | 5, 57, 15 |
5 | 5, 19, 5 |
1, 19, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 1 x 19 x 1 = 2280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2280
Therefore, the GCF of Fractions 35/40,58/57,55/120 is 1/2280
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 40,57,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,57,120) = 1
common factors(in case of two or more numbers have common factors) = 120
GCF(40,57,120) x common factors =1 x 120 = 120
LCM(40,57,120) = ( 40 × 57 × 120 ) / 120
LCM(40,57,120) = 273600 / 120
LCM(40,57,120) = 2280
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 35,58,55?
The HCF of 35,58,55 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 35/40, 58/57, 55/120?
Answer: GCF of Numerators as per given numbers 35/40, 58/57, 55/120 is
GCF of Numerators i.e. for 35,58,55 is 1
LCM of denominators i.e. for 40,57,120 is 2280.
Thus, GCF of Fractions is 1/2280.Finally, GCF of Fractions for 35/40, 58/57, 55/120 is 1/2280.