GCF of 5208/557, 7728/5170
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5208/557, 7728/5170 i.e 168/2879690 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5208/557, 7728/5170.
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 5208/557,7728/5170?
Given fractions are 5208/557,7728/5170
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 5208/557,7728/5170, numerators are 5208,7728
Denominators are 557,5170
The GCF of 5208,7728 is 168 .
LCM of 557,5170 is 2879690.
The greatest common factor of 5208/557,7728/5170 = [GCF of 5208,7728]/[LCM of 557,5170]= 168/2879690
Therefore, the GCF of 5208/557,7728/5170 is 168/2879690.
To find the highest common factor of 5208,7728, we have to find the factors of both numbers and list the highest common factor.
The factors of 5208 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 31, 42, 56, 62, 84, 93, 124, 168, 186, 217, 248, 372, 434, 651, 744, 868, 1302, 1736, 2604, 5208
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 5208,7728 is 168.
Lets's calculate GCF of 5208,7728
| 2 | 5208, 7728 |
| 2 | 2604, 3864 |
| 2 | 1302, 1932 |
| 3 | 651, 966 |
| 7 | 217, 322 |
| 31, 46 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 7 = 168
Greatest Common Factor of 5208,7728 By Matching Biggest Common Factor Method
Now, list down the factors of 5208
:1,2,3,4,6,7,8,12,14,21,24,28,31,42,56,62,84,93,124,168,186,217,248,372,434,651,744,868,1302,1736,2604,5208
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 5208,7728 . The biggest common factor number is the GCF number.
So the greatest common factor 5208,7728 is 168.
Lets's calculate LCM of 557,5170
Given numbers has no common factors except 1. So, there LCM is their product i.e 2879690
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 168/2879690
Therefore, the GCF of Fractions 5208/557,7728/5170 is 168/2879690
Least Common Multiple of 557,5170 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 557,5170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(557,5170) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(557,5170) x common factors =1 x 1 = 1
LCM(557,5170) = ( 557 × 5170 ) / 1
LCM(557,5170) = 2879690 / 1
LCM(557,5170) = 2879690
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 5208/557, 7728/5170
1. What is the HCF of 5208,7728?
The HCF of 5208,7728 is 168
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 5208/557, 7728/5170?
Answer: GCF of Numerators as per given numbers 5208/557, 7728/5170 is
GCF of Numerators i.e. for 5208,7728 is 168
LCM of denominators i.e. for 557,5170 is 2879690.
Thus, GCF of Fractions is 168/2879690.Finally, GCF of Fractions for 5208/557, 7728/5170 is 168/2879690.