GCF of 7456/284, 4112/2544
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7456/284, 4112/2544 i.e 16/180624 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7456/284, 4112/2544.
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 7456/284,4112/2544?
Given fractions are 7456/284,4112/2544
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 7456/284,4112/2544, numerators are 7456,4112
Denominators are 284,2544
The GCF of 7456,4112 is 16 .
LCM of 284,2544 is 180624.
The greatest common factor of 7456/284,4112/2544 = [GCF of 7456,4112]/[LCM of 284,2544]= 16/180624
Therefore, the GCF of 7456/284,4112/2544 is 16/180624.
To find the highest common factor of 7456,4112, we have to find the factors of both numbers and list the highest common factor.
The factors of 7456 are 1, 2, 4, 8, 16, 32, 233, 466, 932, 1864, 3728, 7456
The factors of 4112 are 1, 2, 4, 8, 16, 257, 514, 1028, 2056, 4112
The HCF of 7456,4112 is 16.
Lets's calculate GCF of 7456,4112
| 2 | 7456, 4112 |
| 2 | 3728, 2056 |
| 2 | 1864, 1028 |
| 2 | 932, 514 |
| 466, 257 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 7456,4112 By Matching Biggest Common Factor Method
Now, list down the factors of 7456
:1,2,4,8,16,32,233,466,932,1864,3728,7456
Now, list down the factors of 4112
:1,2,4,8,16,257,514,1028,2056,4112
Greatest Common Factor
We found the factors 7456,4112 . The biggest common factor number is the GCF number.
So the greatest common factor 7456,4112 is 16.
Lets's calculate LCM of 284,2544
| 2 | 284, 2544 |
| 2 | 142, 1272 |
| 71, 636 |
∴ So the LCM of the given numbers is 2 x 2 x 71 x 636 = 180624
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/180624
Therefore, the GCF of Fractions 7456/284,4112/2544 is 16/180624
Least Common Multiple of 284,2544 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 284,2544 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(284,2544) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(284,2544) x common factors =4 x 1 = 4
LCM(284,2544) = ( 284 × 2544 ) / 4
LCM(284,2544) = 722496 / 4
LCM(284,2544) = 180624
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FAQs on GCF of Fractions of 7456/284, 4112/2544
1. What is the HCF of 7456,4112?
The HCF of 7456,4112 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 7456/284, 4112/2544?
Answer: GCF of Numerators as per given numbers 7456/284, 4112/2544 is
GCF of Numerators i.e. for 7456,4112 is 16
LCM of denominators i.e. for 284,2544 is 180624.
Thus, GCF of Fractions is 16/180624.Finally, GCF of Fractions for 7456/284, 4112/2544 is 16/180624.