GCF of 3170/512, 7310/3880
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3170/512, 7310/3880 i.e 10/248320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3170/512, 7310/3880.
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 3170/512,7310/3880?
Given fractions are 3170/512,7310/3880
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 3170/512,7310/3880, numerators are 3170,7310
Denominators are 512,3880
The GCF of 3170,7310 is 10 .
LCM of 512,3880 is 248320.
The greatest common factor of 3170/512,7310/3880 = [GCF of 3170,7310]/[LCM of 512,3880]= 10/248320
Therefore, the GCF of 3170/512,7310/3880 is 10/248320.
To find the highest common factor of 3170,7310, we have to find the factors of both numbers and list the highest common factor.
The factors of 3170 are 1, 2, 5, 10, 317, 634, 1585, 3170
The factors of 7310 are 1, 2, 5, 10, 17, 34, 43, 85, 86, 170, 215, 430, 731, 1462, 3655, 7310
The HCF of 3170,7310 is 10.
Lets's calculate GCF of 3170,7310
| 2 | 3170, 7310 |
| 5 | 1585, 3655 |
| 317, 731 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 3170,7310 By Matching Biggest Common Factor Method
Now, list down the factors of 3170
:1,2,5,10,317,634,1585,3170
Now, list down the factors of 7310
:1,2,5,10,17,34,43,85,86,170,215,430,731,1462,3655,7310
Greatest Common Factor
We found the factors 3170,7310 . The biggest common factor number is the GCF number.
So the greatest common factor 3170,7310 is 10.
Lets's calculate LCM of 512,3880
| 2 | 512, 3880 |
| 2 | 256, 1940 |
| 2 | 128, 970 |
| 64, 485 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 64 x 485 = 248320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/248320
Therefore, the GCF of Fractions 3170/512,7310/3880 is 10/248320
Least Common Multiple of 512,3880 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 512,3880 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,3880) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(512,3880) x common factors =8 x 1 = 8
LCM(512,3880) = ( 512 × 3880 ) / 8
LCM(512,3880) = 1986560 / 8
LCM(512,3880) = 248320
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FAQs on GCF of Fractions of 3170/512, 7310/3880
1. What is the HCF of 3170,7310?
The HCF of 3170,7310 is 10
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 3170/512, 7310/3880?
Answer: GCF of Numerators as per given numbers 3170/512, 7310/3880 is
GCF of Numerators i.e. for 3170,7310 is 10
LCM of denominators i.e. for 512,3880 is 248320.
Thus, GCF of Fractions is 10/248320.Finally, GCF of Fractions for 3170/512, 7310/3880 is 10/248320.