Use our free GCF of Fractions Calculator tool to compute the GCF of 7824/157, 3036/2969 i.e 12/466133 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7824/157, 3036/2969.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7824/157,3036/2969
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 7824/157,3036/2969, numerators are 7824,3036
Denominators are 157,2969
The GCF of 7824,3036 is 12 .
LCM of 157,2969 is 466133.
The greatest common factor of 7824/157,3036/2969 = [GCF of 7824,3036]/[LCM of 157,2969]= 12/466133
Therefore, the GCF of 7824/157,3036/2969 is 12/466133.
To find the highest common factor of 7824,3036, we have to find the factors of both numbers and list the highest common factor.
The factors of 7824 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 163, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 7824
The factors of 3036 are 1, 2, 3, 4, 6, 11, 12, 22, 23, 33, 44, 46, 66, 69, 92, 132, 138, 253, 276, 506, 759, 1012, 1518, 3036
The HCF of 7824,3036 is 12.
Lets's calculate GCF of 7824,3036
2 | 7824, 3036 |
2 | 3912, 1518 |
3 | 1956, 759 |
652, 253 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 7824
:1,2,3,4,6,8,12,16,24,48,163,326,489,652,978,1304,1956,2608,3912,7824
Now, list down the factors of 3036
:1,2,3,4,6,11,12,22,23,33,44,46,66,69,92,132,138,253,276,506,759,1012,1518,3036
Greatest Common Factor
We found the factors 7824,3036 . The biggest common factor number is the GCF number.
So the greatest common factor 7824,3036 is 12.
Lets's calculate LCM of 157,2969
Given numbers has no common factors except 1. So, there LCM is their product i.e 466133
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/466133
Therefore, the GCF of Fractions 7824/157,3036/2969 is 12/466133
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 157,2969 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(157,2969) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(157,2969) x common factors =1 x 1 = 1
LCM(157,2969) = ( 157 × 2969 ) / 1
LCM(157,2969) = 466133 / 1
LCM(157,2969) = 466133
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 7824,3036?
The HCF of 7824,3036 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 7824/157, 3036/2969?
Answer: GCF of Numerators as per given numbers 7824/157, 3036/2969 is
GCF of Numerators i.e. for 7824,3036 is 12
LCM of denominators i.e. for 157,2969 is 466133.
Thus, GCF of Fractions is 12/466133.Finally, GCF of Fractions for 7824/157, 3036/2969 is 12/466133.