GCF of 9975/704, 7728/3825
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9975/704, 7728/3825 i.e 21/2692800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9975/704, 7728/3825.
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 9975/704,7728/3825?
Given fractions are 9975/704,7728/3825
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 9975/704,7728/3825, numerators are 9975,7728
Denominators are 704,3825
The GCF of 9975,7728 is 21 .
LCM of 704,3825 is 2692800.
The greatest common factor of 9975/704,7728/3825 = [GCF of 9975,7728]/[LCM of 704,3825]= 21/2692800
Therefore, the GCF of 9975/704,7728/3825 is 21/2692800.
To find the highest common factor of 9975,7728, we have to find the factors of both numbers and list the highest common factor.
The factors of 9975 are 1, 3, 5, 7, 15, 19, 21, 25, 35, 57, 75, 95, 105, 133, 175, 285, 399, 475, 525, 665, 1425, 1995, 3325, 9975
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 HCF of 9975,7728 is 21.
Lets's calculate GCF of 9975,7728
| 3 | 9975, 7728 |
| 7 | 3325, 2576 |
| 475, 368 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 9975,7728 By Matching Biggest Common Factor Method
Now, list down the factors of 9975
:1,3,5,7,15,19,21,25,35,57,75,95,105,133,175,285,399,475,525,665,1425,1995,3325,9975
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
Greatest Common Factor
We found the factors 9975,7728 . The biggest common factor number is the GCF number.
So the greatest common factor 9975,7728 is 21.
Lets's calculate LCM of 704,3825
Given numbers has no common factors except 1. So, there LCM is their product i.e 2692800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/2692800
Therefore, the GCF of Fractions 9975/704,7728/3825 is 21/2692800
Least Common Multiple of 704,3825 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 704,3825 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(704,3825) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(704,3825) x common factors =1 x 1 = 1
LCM(704,3825) = ( 704 × 3825 ) / 1
LCM(704,3825) = 2692800 / 1
LCM(704,3825) = 2692800
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 9975/704, 7728/3825
1. What is the HCF of 9975,7728?
The HCF of 9975,7728 is 21
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 9975/704, 7728/3825?
Answer: GCF of Numerators as per given numbers 9975/704, 7728/3825 is
GCF of Numerators i.e. for 9975,7728 is 21
LCM of denominators i.e. for 704,3825 is 2692800.
Thus, GCF of Fractions is 21/2692800.Finally, GCF of Fractions for 9975/704, 7728/3825 is 21/2692800.