GCF of 7728/825, 9370/723
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7728/825, 9370/723 i.e 2/198825 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7728/825, 9370/723.
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 7728/825,9370/723?
Given fractions are 7728/825,9370/723
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 7728/825,9370/723, numerators are 7728,9370
Denominators are 825,723
The GCF of 7728,9370 is 2 .
LCM of 825,723 is 198825.
The greatest common factor of 7728/825,9370/723 = [GCF of 7728,9370]/[LCM of 825,723]= 2/198825
Therefore, the GCF of 7728/825,9370/723 is 2/198825.
To find the highest common factor of 7728,9370, we have to find the factors of both numbers and list the highest common factor.
The factors of 7728 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864, 7728
The factors of 9370 are 1, 2, 5, 10, 937, 1874, 4685, 9370
The HCF of 7728,9370 is 2.
Lets's calculate GCF of 7728,9370
| 2 | 7728, 9370 |
| 3864, 4685 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7728,9370 By Matching Biggest Common Factor Method
Now, list down the factors of 7728
:1,2,3,4,6,7,8,12,14,16,21,23,24,28,42,46,48,56,69,84,92,112,138,161,168,184,276,322,336,368,483,552,644,966,1104,1288,1932,2576,3864,7728
Now, list down the factors of 9370
:1,2,5,10,937,1874,4685,9370
Greatest Common Factor
We found the factors 7728,9370 . The biggest common factor number is the GCF number.
So the greatest common factor 7728,9370 is 2.
Lets's calculate LCM of 825,723
| 3 | 825, 723 |
| 275, 241 |
∴ So the LCM of the given numbers is 3 x 275 x 241 = 198825
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/198825
Therefore, the GCF of Fractions 7728/825,9370/723 is 2/198825
Least Common Multiple of 825,723 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 825,723 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(825,723) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(825,723) x common factors =3 x 1 = 3
LCM(825,723) = ( 825 × 723 ) / 3
LCM(825,723) = 596475 / 3
LCM(825,723) = 198825
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FAQs on GCF of Fractions of 7728/825, 9370/723
1. What is the HCF of 7728,9370?
The HCF of 7728,9370 is 2
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 7728/825, 9370/723?
Answer: GCF of Numerators as per given numbers 7728/825, 9370/723 is
GCF of Numerators i.e. for 7728,9370 is 2
LCM of denominators i.e. for 825,723 is 198825.
Thus, GCF of Fractions is 2/198825.Finally, GCF of Fractions for 7728/825, 9370/723 is 2/198825.