Use our free GCF of Fractions Calculator tool to compute the GCF of 77/82, 759/47, 275/114 i.e 11/219678 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/82, 759/47, 275/114.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 77/82,759/47,275/114
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 77/82,759/47,275/114, numerators are 77,759,275
Denominators are 82,47,114
The GCF of 77,759,275 is 11 .
LCM of 82,47,114 is 219678.
The greatest common factor of 77/82,759/47,275/114 = [GCF of 77,759,275]/[LCM of 82,47,114]= 11/219678
Therefore, the GCF of 77/82,759/47,275/114 is 11/219678.
To find the highest common factor of 77,759,275, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 759 are 1, 3, 11, 23, 33, 69, 253, 759
The factors of 275 are 1, 5, 11, 25, 55, 275
The HCF of 77,759,275 is 11.
Lets's calculate GCF of 77,759,275
11 | 77, 759, 275 |
7, 69, 25 |
∴ So the GCF of the given numbers is 11 = 11
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 759
:1,3,11,23,33,69,253,759
Now, list down the factors of 275
:1,5,11,25,55,275
Greatest Common Factor
We found the factors 77,759,275 . The biggest common factor number is the GCF number.
So the greatest common factor 77,759,275 is 11.
Lets's calculate LCM of 82,47,114
2 | 82, 47, 114 |
41, 47, 57 |
∴ So the LCM of the given numbers is 2 x 41 x 47 x 57 = 219678
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/219678
Therefore, the GCF of Fractions 77/82,759/47,275/114 is 11/219678
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 82,47,114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,47,114) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(82,47,114) x common factors =1 x 2 = 2
LCM(82,47,114) = ( 82 × 47 × 114 ) / 2
LCM(82,47,114) = 439356 / 2
LCM(82,47,114) = 219678
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 77,759,275?
The HCF of 77,759,275 is 11
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 77/82, 759/47, 275/114?
Answer: GCF of Numerators as per given numbers 77/82, 759/47, 275/114 is
GCF of Numerators i.e. for 77,759,275 is 11
LCM of denominators i.e. for 82,47,114 is 219678.
Thus, GCF of Fractions is 11/219678.Finally, GCF of Fractions for 77/82, 759/47, 275/114 is 11/219678.