GCF of 7872/287, 7932/1789
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7872/287, 7932/1789 i.e 12/513443 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7872/287, 7932/1789.
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 7872/287,7932/1789?
Given fractions are 7872/287,7932/1789
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 7872/287,7932/1789, numerators are 7872,7932
Denominators are 287,1789
The GCF of 7872,7932 is 12 .
LCM of 287,1789 is 513443.
The greatest common factor of 7872/287,7932/1789 = [GCF of 7872,7932]/[LCM of 287,1789]= 12/513443
Therefore, the GCF of 7872/287,7932/1789 is 12/513443.
To find the highest common factor of 7872,7932, we have to find the factors of both numbers and list the highest common factor.
The factors of 7872 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 41, 48, 64, 82, 96, 123, 164, 192, 246, 328, 492, 656, 984, 1312, 1968, 2624, 3936, 7872
The factors of 7932 are 1, 2, 3, 4, 6, 12, 661, 1322, 1983, 2644, 3966, 7932
The HCF of 7872,7932 is 12.
Lets's calculate GCF of 7872,7932
| 2 | 7872, 7932 |
| 2 | 3936, 3966 |
| 3 | 1968, 1983 |
| 656, 661 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 7872,7932 By Matching Biggest Common Factor Method
Now, list down the factors of 7872
:1,2,3,4,6,8,12,16,24,32,41,48,64,82,96,123,164,192,246,328,492,656,984,1312,1968,2624,3936,7872
Now, list down the factors of 7932
:1,2,3,4,6,12,661,1322,1983,2644,3966,7932
Greatest Common Factor
We found the factors 7872,7932 . The biggest common factor number is the GCF number.
So the greatest common factor 7872,7932 is 12.
Lets's calculate LCM of 287,1789
Given numbers has no common factors except 1. So, there LCM is their product i.e 513443
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/513443
Therefore, the GCF of Fractions 7872/287,7932/1789 is 12/513443
Least Common Multiple of 287,1789 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 287,1789 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(287,1789) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(287,1789) x common factors =1 x 1 = 1
LCM(287,1789) = ( 287 × 1789 ) / 1
LCM(287,1789) = 513443 / 1
LCM(287,1789) = 513443
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FAQs on GCF of Fractions of 7872/287, 7932/1789
1. What is the HCF of 7872,7932?
The HCF of 7872,7932 is 12
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 7872/287, 7932/1789?
Answer: GCF of Numerators as per given numbers 7872/287, 7932/1789 is
GCF of Numerators i.e. for 7872,7932 is 12
LCM of denominators i.e. for 287,1789 is 513443.
Thus, GCF of Fractions is 12/513443.Finally, GCF of Fractions for 7872/287, 7932/1789 is 12/513443.