GCF of 640/827, 256/174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 640/827, 256/174 i.e 128/143898 easily. The following is the detailed procedure to determine the greatest common factor of fractions 640/827, 256/174.
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 640/827,256/174?
Given fractions are 640/827,256/174
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 640/827,256/174, numerators are 640,256
Denominators are 827,174
The GCF of 640,256 is 128 .
LCM of 827,174 is 143898.
The greatest common factor of 640/827,256/174 = [GCF of 640,256]/[LCM of 827,174]= 128/143898
Therefore, the GCF of 640/827,256/174 is 128/143898.
To find the highest common factor of 640,256, we have to find the factors of both numbers and list the highest common factor.
The factors of 640 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256
The HCF of 640,256 is 128.
Lets's calculate GCF of 640,256
| 2 | 640, 256 |
| 2 | 320, 128 |
| 2 | 160, 64 |
| 2 | 80, 32 |
| 2 | 40, 16 |
| 2 | 20, 8 |
| 2 | 10, 4 |
| 5, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128
Greatest Common Factor of 640,256 By Matching Biggest Common Factor Method
Now, list down the factors of 640
:1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640
Now, list down the factors of 256
:1,2,4,8,16,32,64,128,256
Greatest Common Factor
We found the factors 640,256 . The biggest common factor number is the GCF number.
So the greatest common factor 640,256 is 128.
Lets's calculate LCM of 827,174
Given numbers has no common factors except 1. So, there LCM is their product i.e 143898
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 128/143898
Therefore, the GCF of Fractions 640/827,256/174 is 128/143898
Least Common Multiple of 827,174 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 827,174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(827,174) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(827,174) x common factors =1 x 1 = 1
LCM(827,174) = ( 827 × 174 ) / 1
LCM(827,174) = 143898 / 1
LCM(827,174) = 143898
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FAQs on GCF of Fractions of 640/827, 256/174
1. What is the HCF of 640,256?
The HCF of 640,256 is 128
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 640/827, 256/174?
Answer: GCF of Numerators as per given numbers 640/827, 256/174 is
GCF of Numerators i.e. for 640,256 is 128
LCM of denominators i.e. for 827,174 is 143898.
Thus, GCF of Fractions is 128/143898.Finally, GCF of Fractions for 640/827, 256/174 is 128/143898.