Use our free GCF of Fractions Calculator tool to compute the GCF of 31/75, 59/40, 55/88, 63/75 i.e 1/6600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/75, 59/40, 55/88, 63/75.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 31/75,59/40,55/88,63/75
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 31/75,59/40,55/88,63/75, numerators are 31,59,55,63
Denominators are 75,40,88,75
The GCF of 31,59,55,63 is 1 .
LCM of 75,40,88,75 is 6600.
The greatest common factor of 31/75,59/40,55/88,63/75 = [GCF of 31,59,55,63]/[LCM of 75,40,88,75]= 1/6600
Therefore, the GCF of 31/75,59/40,55/88,63/75 is 1/6600.
To find the highest common factor of 31,59,55,63, we have to find the factors of both numbers and list the highest common factor.
The factors of 31 are 1, 31
The factors of 59 are 1, 59
The factors of 55 are 1, 5, 11, 55
The factors of 63 are 1, 3, 7, 9, 21, 63
The HCF of 31,59,55,63 is 1.
Lets's calculate GCF of 31,59,55,63
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 31
:1,31
Now, list down the factors of 59
:1,59
Now, list down the factors of 55
:1,5,11,55
Now, list down the factors of 63
:1,3,7,9,21,63
Greatest Common Factor
We found the factors 31,59,55,63 . The biggest common factor number is the GCF number.
So the greatest common factor 31,59,55,63 is 1.
Lets's calculate LCM of 75,40,88,75
2 | 75, 40, 88, 75 |
2 | 75, 20, 44, 75 |
2 | 75, 10, 22, 75 |
3 | 75, 5, 11, 75 |
5 | 25, 5, 11, 25 |
5 | 1, 5, 11, 5 |
1, 1, 11, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 5 x 1 x 1 x 11 x 1 = 6600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6600
Therefore, the GCF of Fractions 31/75,59/40,55/88,63/75 is 1/6600
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 75,40,88,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,40,88,75) = 1
common factors(in case of two or more numbers have common factors) = 3000
GCF(75,40,88,75) x common factors =1 x 3000 = 3000
LCM(75,40,88,75) = ( 75 × 40 × 88 × 75 ) / 3000
LCM(75,40,88,75) = 19800000 / 3000
LCM(75,40,88,75) = 6600
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 31,59,55,63?
The HCF of 31,59,55,63 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 31/75, 59/40, 55/88, 63/75?
Answer: GCF of Numerators as per given numbers 31/75, 59/40, 55/88, 63/75 is
GCF of Numerators i.e. for 31,59,55,63 is 1
LCM of denominators i.e. for 75,40,88,75 is 6600.
Thus, GCF of Fractions is 1/6600.Finally, GCF of Fractions for 31/75, 59/40, 55/88, 63/75 is 1/6600.