GCF of 7176/290, 7740/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7176/290, 7740/728 i.e 12/105560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7176/290, 7740/728.
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 7176/290,7740/728?
Given fractions are 7176/290,7740/728
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 7176/290,7740/728, numerators are 7176,7740
Denominators are 290,728
The GCF of 7176,7740 is 12 .
LCM of 290,728 is 105560.
The greatest common factor of 7176/290,7740/728 = [GCF of 7176,7740]/[LCM of 290,728]= 12/105560
Therefore, the GCF of 7176/290,7740/728 is 12/105560.
To find the highest common factor of 7176,7740, we have to find the factors of both numbers and list the highest common factor.
The factors of 7176 are 1, 2, 3, 4, 6, 8, 12, 13, 23, 24, 26, 39, 46, 52, 69, 78, 92, 104, 138, 156, 184, 276, 299, 312, 552, 598, 897, 1196, 1794, 2392, 3588, 7176
The factors of 7740 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 43, 45, 60, 86, 90, 129, 172, 180, 215, 258, 387, 430, 516, 645, 774, 860, 1290, 1548, 1935, 2580, 3870, 7740
The HCF of 7176,7740 is 12.
Lets's calculate GCF of 7176,7740
| 2 | 7176, 7740 |
| 2 | 3588, 3870 |
| 3 | 1794, 1935 |
| 598, 645 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 7176,7740 By Matching Biggest Common Factor Method
Now, list down the factors of 7176
:1,2,3,4,6,8,12,13,23,24,26,39,46,52,69,78,92,104,138,156,184,276,299,312,552,598,897,1196,1794,2392,3588,7176
Now, list down the factors of 7740
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,43,45,60,86,90,129,172,180,215,258,387,430,516,645,774,860,1290,1548,1935,2580,3870,7740
Greatest Common Factor
We found the factors 7176,7740 . The biggest common factor number is the GCF number.
So the greatest common factor 7176,7740 is 12.
Lets's calculate LCM of 290,728
| 2 | 290, 728 |
| 145, 364 |
∴ So the LCM of the given numbers is 2 x 145 x 364 = 105560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/105560
Therefore, the GCF of Fractions 7176/290,7740/728 is 12/105560
Least Common Multiple of 290,728 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 290,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(290,728) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(290,728) x common factors =2 x 1 = 2
LCM(290,728) = ( 290 × 728 ) / 2
LCM(290,728) = 211120 / 2
LCM(290,728) = 105560
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FAQs on GCF of Fractions of 7176/290, 7740/728
1. What is the HCF of 7176,7740?
The HCF of 7176,7740 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 7176/290, 7740/728?
Answer: GCF of Numerators as per given numbers 7176/290, 7740/728 is
GCF of Numerators i.e. for 7176,7740 is 12
LCM of denominators i.e. for 290,728 is 105560.
Thus, GCF of Fractions is 12/105560.Finally, GCF of Fractions for 7176/290, 7740/728 is 12/105560.