Use our free GCF of Fractions Calculator tool to compute the GCF of 33/752, 31/784, 261/709 i.e 1/26125232 easily. The following is the detailed procedure to determine the greatest common factor of fractions 33/752, 31/784, 261/709.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 33/752,31/784,261/709
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 33/752,31/784,261/709, numerators are 33,31,261
Denominators are 752,784,709
The GCF of 33,31,261 is 1 .
LCM of 752,784,709 is 26125232.
The greatest common factor of 33/752,31/784,261/709 = [GCF of 33,31,261]/[LCM of 752,784,709]= 1/26125232
Therefore, the GCF of 33/752,31/784,261/709 is 1/26125232.
To find the highest common factor of 33,31,261, we have to find the factors of both numbers and list the highest common factor.
The factors of 33 are 1, 3, 11, 33
The factors of 31 are 1, 31
The factors of 261 are 1, 3, 9, 29, 87, 261
The HCF of 33,31,261 is 1.
Lets's calculate GCF of 33,31,261
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 33
:1,3,11,33
Now, list down the factors of 31
:1,31
Now, list down the factors of 261
:1,3,9,29,87,261
Greatest Common Factor
We found the factors 33,31,261 . The biggest common factor number is the GCF number.
So the greatest common factor 33,31,261 is 1.
Lets's calculate LCM of 752,784,709
2 | 752, 784, 709 |
2 | 376, 392, 709 |
2 | 188, 196, 709 |
2 | 94, 98, 709 |
47, 49, 709 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 47 x 49 x 709 = 26125232
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26125232
Therefore, the GCF of Fractions 33/752,31/784,261/709 is 1/26125232
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 752,784,709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(752,784,709) = 1
common factors(in case of two or more numbers have common factors) = 16
GCF(752,784,709) x common factors =1 x 16 = 16
LCM(752,784,709) = ( 752 × 784 × 709 ) / 16
LCM(752,784,709) = 418003712 / 16
LCM(752,784,709) = 26125232
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 33,31,261?
The HCF of 33,31,261 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 33/752, 31/784, 261/709?
Answer: GCF of Numerators as per given numbers 33/752, 31/784, 261/709 is
GCF of Numerators i.e. for 33,31,261 is 1
LCM of denominators i.e. for 752,784,709 is 26125232.
Thus, GCF of Fractions is 1/26125232.Finally, GCF of Fractions for 33/752, 31/784, 261/709 is 1/26125232.