GCF of 7710/166, 5640/9504
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7710/166, 5640/9504 i.e 30/788832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7710/166, 5640/9504.
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 7710/166,5640/9504?
Given fractions are 7710/166,5640/9504
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 7710/166,5640/9504, numerators are 7710,5640
Denominators are 166,9504
The GCF of 7710,5640 is 30 .
LCM of 166,9504 is 788832.
The greatest common factor of 7710/166,5640/9504 = [GCF of 7710,5640]/[LCM of 166,9504]= 30/788832
Therefore, the GCF of 7710/166,5640/9504 is 30/788832.
To find the highest common factor of 7710,5640, we have to find the factors of both numbers and list the highest common factor.
The factors of 7710 are 1, 2, 3, 5, 6, 10, 15, 30, 257, 514, 771, 1285, 1542, 2570, 3855, 7710
The factors of 5640 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 47, 60, 94, 120, 141, 188, 235, 282, 376, 470, 564, 705, 940, 1128, 1410, 1880, 2820, 5640
The HCF of 7710,5640 is 30.
Lets's calculate GCF of 7710,5640
| 2 | 7710, 5640 |
| 3 | 3855, 2820 |
| 5 | 1285, 940 |
| 257, 188 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 7710,5640 By Matching Biggest Common Factor Method
Now, list down the factors of 7710
:1,2,3,5,6,10,15,30,257,514,771,1285,1542,2570,3855,7710
Now, list down the factors of 5640
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,47,60,94,120,141,188,235,282,376,470,564,705,940,1128,1410,1880,2820,5640
Greatest Common Factor
We found the factors 7710,5640 . The biggest common factor number is the GCF number.
So the greatest common factor 7710,5640 is 30.
Lets's calculate LCM of 166,9504
| 2 | 166, 9504 |
| 83, 4752 |
∴ So the LCM of the given numbers is 2 x 83 x 4752 = 788832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/788832
Therefore, the GCF of Fractions 7710/166,5640/9504 is 30/788832
Least Common Multiple of 166,9504 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 166,9504 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(166,9504) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(166,9504) x common factors =2 x 1 = 2
LCM(166,9504) = ( 166 × 9504 ) / 2
LCM(166,9504) = 1577664 / 2
LCM(166,9504) = 788832
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FAQs on GCF of Fractions of 7710/166, 5640/9504
1. What is the HCF of 7710,5640?
The HCF of 7710,5640 is 30
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 7710/166, 5640/9504?
Answer: GCF of Numerators as per given numbers 7710/166, 5640/9504 is
GCF of Numerators i.e. for 7710,5640 is 30
LCM of denominators i.e. for 166,9504 is 788832.
Thus, GCF of Fractions is 30/788832.Finally, GCF of Fractions for 7710/166, 5640/9504 is 30/788832.