Use our free GCF of Fractions Calculator tool to compute the GCF of 75/68, 78/952, 716/904 i.e 1/107576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/68, 78/952, 716/904.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/68,78/952,716/904
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 75/68,78/952,716/904, numerators are 75,78,716
Denominators are 68,952,904
The GCF of 75,78,716 is 1 .
LCM of 68,952,904 is 107576.
The greatest common factor of 75/68,78/952,716/904 = [GCF of 75,78,716]/[LCM of 68,952,904]= 1/107576
Therefore, the GCF of 75/68,78/952,716/904 is 1/107576.
To find the highest common factor of 75,78,716, we have to find the factors of both numbers and list the highest common factor.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 716 are 1, 2, 4, 179, 358, 716
The HCF of 75,78,716 is 1.
Lets's calculate GCF of 75,78,716
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 716
:1,2,4,179,358,716
Greatest Common Factor
We found the factors 75,78,716 . The biggest common factor number is the GCF number.
So the greatest common factor 75,78,716 is 1.
Lets's calculate LCM of 68,952,904
2 | 68, 952, 904 |
2 | 34, 476, 452 |
2 | 17, 238, 226 |
17 | 17, 119, 113 |
1, 7, 113 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 17 x 1 x 7 x 113 = 107576
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/107576
Therefore, the GCF of Fractions 75/68,78/952,716/904 is 1/107576
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 68,952,904 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,952,904) = 4
common factors(in case of two or more numbers have common factors) = 136
GCF(68,952,904) x common factors =4 x 136 = 544
LCM(68,952,904) = ( 68 × 952 × 904 ) / 544
LCM(68,952,904) = 58521344 / 544
LCM(68,952,904) = 107576
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 75,78,716?
The HCF of 75,78,716 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 75/68, 78/952, 716/904?
Answer: GCF of Numerators as per given numbers 75/68, 78/952, 716/904 is
GCF of Numerators i.e. for 75,78,716 is 1
LCM of denominators i.e. for 68,952,904 is 107576.
Thus, GCF of Fractions is 1/107576.Finally, GCF of Fractions for 75/68, 78/952, 716/904 is 1/107576.