GCF of 784/434, 3152/318
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 784/434, 3152/318 i.e 16/69006 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/434, 3152/318.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 784/434,3152/318?
Given fractions are 784/434,3152/318
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 784/434,3152/318, numerators are 784,3152
Denominators are 434,318
The GCF of 784,3152 is 16 .
LCM of 434,318 is 69006.
The greatest common factor of 784/434,3152/318 = [GCF of 784,3152]/[LCM of 434,318]= 16/69006
Therefore, the GCF of 784/434,3152/318 is 16/69006.
To find the highest common factor of 784,3152, 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 3152 are 1, 2, 4, 8, 16, 197, 394, 788, 1576, 3152
The HCF of 784,3152 is 16.
Lets's calculate GCF of 784,3152
| 2 | 784, 3152 |
| 2 | 392, 1576 |
| 2 | 196, 788 |
| 2 | 98, 394 |
| 49, 197 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 784,3152 By Matching Biggest Common Factor Method
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 3152
:1,2,4,8,16,197,394,788,1576,3152
Greatest Common Factor
We found the factors 784,3152 . The biggest common factor number is the GCF number.
So the greatest common factor 784,3152 is 16.
Lets's calculate LCM of 434,318
| 2 | 434, 318 |
| 217, 159 |
∴ So the LCM of the given numbers is 2 x 217 x 159 = 69006
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/69006
Therefore, the GCF of Fractions 784/434,3152/318 is 16/69006
Least Common Multiple of 434,318 with GCF Formula
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 434,318 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(434,318) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(434,318) x common factors =2 x 1 = 2
LCM(434,318) = ( 434 × 318 ) / 2
LCM(434,318) = 138012 / 2
LCM(434,318) = 69006
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 784/434, 3152/318
1. What is the HCF of 784,3152?
The HCF of 784,3152 is 16
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 784/434, 3152/318?
Answer: GCF of Numerators as per given numbers 784/434, 3152/318 is
GCF of Numerators i.e. for 784,3152 is 16
LCM of denominators i.e. for 434,318 is 69006.
Thus, GCF of Fractions is 16/69006.Finally, GCF of Fractions for 784/434, 3152/318 is 16/69006.