GCF of 438/784, 810/256
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 438/784, 810/256 i.e 6/12544 easily. The following is the detailed procedure to determine the greatest common factor of fractions 438/784, 810/256.
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 438/784,810/256?
Given fractions are 438/784,810/256
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 438/784,810/256, numerators are 438,810
Denominators are 784,256
The GCF of 438,810 is 6 .
LCM of 784,256 is 12544.
The greatest common factor of 438/784,810/256 = [GCF of 438,810]/[LCM of 784,256]= 6/12544
Therefore, the GCF of 438/784,810/256 is 6/12544.
To find the highest common factor of 438,810, we have to find the factors of both numbers and list the highest common factor.
The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The HCF of 438,810 is 6.
Lets's calculate GCF of 438,810
| 2 | 438, 810 |
| 3 | 219, 405 |
| 73, 135 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 438,810 By Matching Biggest Common Factor Method
Now, list down the factors of 438
:1,2,3,6,73,146,219,438
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Greatest Common Factor
We found the factors 438,810 . The biggest common factor number is the GCF number.
So the greatest common factor 438,810 is 6.
Lets's calculate LCM of 784,256
| 2 | 784, 256 |
| 2 | 392, 128 |
| 2 | 196, 64 |
| 2 | 98, 32 |
| 49, 16 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 49 x 16 = 12544
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/12544
Therefore, the GCF of Fractions 438/784,810/256 is 6/12544
Least Common Multiple of 784,256 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 784,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(784,256) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(784,256) x common factors =16 x 1 = 16
LCM(784,256) = ( 784 × 256 ) / 16
LCM(784,256) = 200704 / 16
LCM(784,256) = 12544
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FAQs on GCF of Fractions of 438/784, 810/256
1. What is the HCF of 438,810?
The HCF of 438,810 is 6
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 438/784, 810/256?
Answer: GCF of Numerators as per given numbers 438/784, 810/256 is
GCF of Numerators i.e. for 438,810 is 6
LCM of denominators i.e. for 784,256 is 12544.
Thus, GCF of Fractions is 6/12544.Finally, GCF of Fractions for 438/784, 810/256 is 6/12544.