GCF of 232/687, 960/309
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 232/687, 960/309 i.e 8/70761 easily. The following is the detailed procedure to determine the greatest common factor of fractions 232/687, 960/309.
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 232/687,960/309?
Given fractions are 232/687,960/309
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 232/687,960/309, numerators are 232,960
Denominators are 687,309
The GCF of 232,960 is 8 .
LCM of 687,309 is 70761.
The greatest common factor of 232/687,960/309 = [GCF of 232,960]/[LCM of 687,309]= 8/70761
Therefore, the GCF of 232/687,960/309 is 8/70761.
To find the highest common factor of 232,960, we have to find the factors of both numbers and list the highest common factor.
The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232
The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
The HCF of 232,960 is 8.
Lets's calculate GCF of 232,960
| 2 | 232, 960 |
| 2 | 116, 480 |
| 2 | 58, 240 |
| 29, 120 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 232,960 By Matching Biggest Common Factor Method
Now, list down the factors of 232
:1,2,4,8,29,58,116,232
Now, list down the factors of 960
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960
Greatest Common Factor
We found the factors 232,960 . The biggest common factor number is the GCF number.
So the greatest common factor 232,960 is 8.
Lets's calculate LCM of 687,309
| 3 | 687, 309 |
| 229, 103 |
∴ So the LCM of the given numbers is 3 x 229 x 103 = 70761
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/70761
Therefore, the GCF of Fractions 232/687,960/309 is 8/70761
Least Common Multiple of 687,309 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 687,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(687,309) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(687,309) x common factors =3 x 1 = 3
LCM(687,309) = ( 687 × 309 ) / 3
LCM(687,309) = 212283 / 3
LCM(687,309) = 70761
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FAQs on GCF of Fractions of 232/687, 960/309
1. What is the HCF of 232,960?
The HCF of 232,960 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 232/687, 960/309?
Answer: GCF of Numerators as per given numbers 232/687, 960/309 is
GCF of Numerators i.e. for 232,960 is 8
LCM of denominators i.e. for 687,309 is 70761.
Thus, GCF of Fractions is 8/70761.Finally, GCF of Fractions for 232/687, 960/309 is 8/70761.