Use our free GCF of Fractions Calculator tool to compute the GCF of 24/756, 1716/9970 i.e 12/3768660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 24/756, 1716/9970.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 24/756,1716/9970
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 24/756,1716/9970, numerators are 24,1716
Denominators are 756,9970
The GCF of 24,1716 is 12 .
LCM of 756,9970 is 3768660.
The greatest common factor of 24/756,1716/9970 = [GCF of 24,1716]/[LCM of 756,9970]= 12/3768660
Therefore, the GCF of 24/756,1716/9970 is 12/3768660.
To find the highest common factor of 24,1716, we have to find the factors of both numbers and list the highest common factor.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The factors of 1716 are 1, 2, 3, 4, 6, 11, 12, 13, 22, 26, 33, 39, 44, 52, 66, 78, 132, 143, 156, 286, 429, 572, 858, 1716
The HCF of 24,1716 is 12.
Lets's calculate GCF of 24,1716
2 | 24, 1716 |
2 | 12, 858 |
3 | 6, 429 |
2, 143 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 24
:1,2,3,4,6,8,12,24
Now, list down the factors of 1716
:1,2,3,4,6,11,12,13,22,26,33,39,44,52,66,78,132,143,156,286,429,572,858,1716
Greatest Common Factor
We found the factors 24,1716 . The biggest common factor number is the GCF number.
So the greatest common factor 24,1716 is 12.
Lets's calculate LCM of 756,9970
2 | 756, 9970 |
378, 4985 |
∴ So the LCM of the given numbers is 2 x 378 x 4985 = 3768660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/3768660
Therefore, the GCF of Fractions 24/756,1716/9970 is 12/3768660
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 756,9970 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(756,9970) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(756,9970) x common factors =2 x 1 = 2
LCM(756,9970) = ( 756 × 9970 ) / 2
LCM(756,9970) = 7537320 / 2
LCM(756,9970) = 3768660
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 24,1716?
The HCF of 24,1716 is 12
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 24/756, 1716/9970?
Answer: GCF of Numerators as per given numbers 24/756, 1716/9970 is
GCF of Numerators i.e. for 24,1716 is 12
LCM of denominators i.e. for 756,9970 is 3768660.
Thus, GCF of Fractions is 12/3768660.Finally, GCF of Fractions for 24/756, 1716/9970 is 12/3768660.