GCF of 256/71, 728/8544
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 256/71, 728/8544 i.e 8/606624 easily. The following is the detailed procedure to determine the greatest common factor of fractions 256/71, 728/8544.
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 256/71,728/8544?
Given fractions are 256/71,728/8544
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 256/71,728/8544, numerators are 256,728
Denominators are 71,8544
The GCF of 256,728 is 8 .
LCM of 71,8544 is 606624.
The greatest common factor of 256/71,728/8544 = [GCF of 256,728]/[LCM of 71,8544]= 8/606624
Therefore, the GCF of 256/71,728/8544 is 8/606624.
To find the highest common factor of 256,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 256,728 is 8.
Lets's calculate GCF of 256,728
| 2 | 256, 728 |
| 2 | 128, 364 |
| 2 | 64, 182 |
| 32, 91 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 256,728 By Matching Biggest Common Factor Method
Now, list down the factors of 256
:1,2,4,8,16,32,64,128,256
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 256,728 . The biggest common factor number is the GCF number.
So the greatest common factor 256,728 is 8.
Lets's calculate LCM of 71,8544
Given numbers has no common factors except 1. So, there LCM is their product i.e 606624
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/606624
Therefore, the GCF of Fractions 256/71,728/8544 is 8/606624
Least Common Multiple of 71,8544 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 71,8544 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,8544) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,8544) x common factors =1 x 1 = 1
LCM(71,8544) = ( 71 × 8544 ) / 1
LCM(71,8544) = 606624 / 1
LCM(71,8544) = 606624
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FAQs on GCF of Fractions of 256/71, 728/8544
1. What is the HCF of 256,728?
The HCF of 256,728 is 8
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 256/71, 728/8544?
Answer: GCF of Numerators as per given numbers 256/71, 728/8544 is
GCF of Numerators i.e. for 256,728 is 8
LCM of denominators i.e. for 71,8544 is 606624.
Thus, GCF of Fractions is 8/606624.Finally, GCF of Fractions for 256/71, 728/8544 is 8/606624.