Use our free GCF of Fractions Calculator tool to compute the GCF of 784/158, 129/916 i.e 1/72364 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/158, 129/916.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 784/158,129/916
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 784/158,129/916, numerators are 784,129
Denominators are 158,916
The GCF of 784,129 is 1 .
LCM of 158,916 is 72364.
The greatest common factor of 784/158,129/916 = [GCF of 784,129]/[LCM of 158,916]= 1/72364
Therefore, the GCF of 784/158,129/916 is 1/72364.
To find the highest common factor of 784,129, we have to find the factors of both numbers and list the highest common factor.
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The factors of 129 are 1, 3, 43, 129
The HCF of 784,129 is 1.
Lets's calculate GCF of 784,129
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Now, list down the factors of 129
:1,3,43,129
Greatest Common Factor
We found the factors 784,129 . The biggest common factor number is the GCF number.
So the greatest common factor 784,129 is 1.
Lets's calculate LCM of 158,916
2 | 158, 916 |
79, 458 |
∴ So the LCM of the given numbers is 2 x 79 x 458 = 72364
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/72364
Therefore, the GCF of Fractions 784/158,129/916 is 1/72364
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 158,916 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(158,916) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(158,916) x common factors =2 x 1 = 2
LCM(158,916) = ( 158 × 916 ) / 2
LCM(158,916) = 144728 / 2
LCM(158,916) = 72364
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 784,129?
The HCF of 784,129 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 784/158, 129/916?
Answer: GCF of Numerators as per given numbers 784/158, 129/916 is
GCF of Numerators i.e. for 784,129 is 1
LCM of denominators i.e. for 158,916 is 72364.
Thus, GCF of Fractions is 1/72364.Finally, GCF of Fractions for 784/158, 129/916 is 1/72364.