GCF of 342/176, 8361/256
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 342/176, 8361/256 i.e 9/2816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/176, 8361/256.
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 342/176,8361/256?
Given fractions are 342/176,8361/256
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 342/176,8361/256, numerators are 342,8361
Denominators are 176,256
The GCF of 342,8361 is 9 .
LCM of 176,256 is 2816.
The greatest common factor of 342/176,8361/256 = [GCF of 342,8361]/[LCM of 176,256]= 9/2816
Therefore, the GCF of 342/176,8361/256 is 9/2816.
To find the highest common factor of 342,8361, we have to find the factors of both numbers and list the highest common factor.
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The factors of 8361 are 1, 3, 9, 929, 2787, 8361
The HCF of 342,8361 is 9.
Lets's calculate GCF of 342,8361
| 3 | 342, 8361 |
| 3 | 114, 2787 |
| 38, 929 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 342,8361 By Matching Biggest Common Factor Method
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Now, list down the factors of 8361
:1,3,9,929,2787,8361
Greatest Common Factor
We found the factors 342,8361 . The biggest common factor number is the GCF number.
So the greatest common factor 342,8361 is 9.
Lets's calculate LCM of 176,256
| 2 | 176, 256 |
| 2 | 88, 128 |
| 2 | 44, 64 |
| 2 | 22, 32 |
| 11, 16 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 11 x 16 = 2816
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/2816
Therefore, the GCF of Fractions 342/176,8361/256 is 9/2816
Least Common Multiple of 176,256 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 176,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(176,256) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(176,256) x common factors =16 x 1 = 16
LCM(176,256) = ( 176 × 256 ) / 16
LCM(176,256) = 45056 / 16
LCM(176,256) = 2816
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FAQs on GCF of Fractions of 342/176, 8361/256
1. What is the HCF of 342,8361?
The HCF of 342,8361 is 9
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 342/176, 8361/256?
Answer: GCF of Numerators as per given numbers 342/176, 8361/256 is
GCF of Numerators i.e. for 342,8361 is 9
LCM of denominators i.e. for 176,256 is 2816.
Thus, GCF of Fractions is 9/2816.Finally, GCF of Fractions for 342/176, 8361/256 is 9/2816.