Use our free GCF of Fractions Calculator tool to compute the GCF of 2312/787, 4512/9416 i.e 8/7410392 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2312/787, 4512/9416.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 2312/787,4512/9416
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 2312/787,4512/9416, numerators are 2312,4512
Denominators are 787,9416
The GCF of 2312,4512 is 8 .
LCM of 787,9416 is 7410392.
The greatest common factor of 2312/787,4512/9416 = [GCF of 2312,4512]/[LCM of 787,9416]= 8/7410392
Therefore, the GCF of 2312/787,4512/9416 is 8/7410392.
To find the highest common factor of 2312,4512, we have to find the factors of both numbers and list the highest common factor.
The factors of 2312 are 1, 2, 4, 8, 17, 34, 68, 136, 289, 578, 1156, 2312
The factors of 4512 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 47, 48, 94, 96, 141, 188, 282, 376, 564, 752, 1128, 1504, 2256, 4512
The HCF of 2312,4512 is 8.
Lets's calculate GCF of 2312,4512
2 | 2312, 4512 |
2 | 1156, 2256 |
2 | 578, 1128 |
289, 564 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 2312
:1,2,4,8,17,34,68,136,289,578,1156,2312
Now, list down the factors of 4512
:1,2,3,4,6,8,12,16,24,32,47,48,94,96,141,188,282,376,564,752,1128,1504,2256,4512
Greatest Common Factor
We found the factors 2312,4512 . The biggest common factor number is the GCF number.
So the greatest common factor 2312,4512 is 8.
Lets's calculate LCM of 787,9416
Given numbers has no common factors except 1. So, there LCM is their product i.e 7410392
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/7410392
Therefore, the GCF of Fractions 2312/787,4512/9416 is 8/7410392
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 787,9416 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(787,9416) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(787,9416) x common factors =1 x 1 = 1
LCM(787,9416) = ( 787 × 9416 ) / 1
LCM(787,9416) = 7410392 / 1
LCM(787,9416) = 7410392
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 2312,4512?
The HCF of 2312,4512 is 8
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 2312/787, 4512/9416?
Answer: GCF of Numerators as per given numbers 2312/787, 4512/9416 is
GCF of Numerators i.e. for 2312,4512 is 8
LCM of denominators i.e. for 787,9416 is 7410392.
Thus, GCF of Fractions is 8/7410392.Finally, GCF of Fractions for 2312/787, 4512/9416 is 8/7410392.