Use our free GCF of Fractions Calculator tool to compute the GCF of 40/108, 696/756, 308/350 i.e 4/18900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/108, 696/756, 308/350.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 40/108,696/756,308/350
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 40/108,696/756,308/350, numerators are 40,696,308
Denominators are 108,756,350
The GCF of 40,696,308 is 4 .
LCM of 108,756,350 is 18900.
The greatest common factor of 40/108,696/756,308/350 = [GCF of 40,696,308]/[LCM of 108,756,350]= 4/18900
Therefore, the GCF of 40/108,696/756,308/350 is 4/18900.
To find the highest common factor of 40,696,308, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 696 are 1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, 696
The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
The HCF of 40,696,308 is 4.
Lets's calculate GCF of 40,696,308
2 | 40, 696, 308 |
2 | 20, 348, 154 |
10, 174, 77 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 696
:1,2,3,4,6,8,12,24,29,58,87,116,174,232,348,696
Now, list down the factors of 308
:1,2,4,7,11,14,22,28,44,77,154,308
Greatest Common Factor
We found the factors 40,696,308 . The biggest common factor number is the GCF number.
So the greatest common factor 40,696,308 is 4.
Lets's calculate LCM of 108,756,350
2 | 108, 756, 350 |
2 | 54, 378, 175 |
3 | 27, 189, 175 |
3 | 9, 63, 175 |
3 | 3, 21, 175 |
7 | 1, 7, 175 |
1, 1, 25 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 3 x 7 x 1 x 1 x 25 = 18900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/18900
Therefore, the GCF of Fractions 40/108,696/756,308/350 is 4/18900
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 108,756,350 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(108,756,350) = 2
common factors(in case of two or more numbers have common factors) = 756
GCF(108,756,350) x common factors =2 x 756 = 1512
LCM(108,756,350) = ( 108 × 756 × 350 ) / 1512
LCM(108,756,350) = 28576800 / 1512
LCM(108,756,350) = 18900
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 40,696,308?
The HCF of 40,696,308 is 4
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 40/108, 696/756, 308/350?
Answer: GCF of Numerators as per given numbers 40/108, 696/756, 308/350 is
GCF of Numerators i.e. for 40,696,308 is 4
LCM of denominators i.e. for 108,756,350 is 18900.
Thus, GCF of Fractions is 4/18900.Finally, GCF of Fractions for 40/108, 696/756, 308/350 is 4/18900.