GCF of 7752/560, 7616/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7752/560, 7616/814 i.e 136/227920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7752/560, 7616/814.
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 7752/560,7616/814?
Given fractions are 7752/560,7616/814
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 7752/560,7616/814, numerators are 7752,7616
Denominators are 560,814
The GCF of 7752,7616 is 136 .
LCM of 560,814 is 227920.
The greatest common factor of 7752/560,7616/814 = [GCF of 7752,7616]/[LCM of 560,814]= 136/227920
Therefore, the GCF of 7752/560,7616/814 is 136/227920.
To find the highest common factor of 7752,7616, we have to find the factors of both numbers and list the highest common factor.
The factors of 7752 are 1, 2, 3, 4, 6, 8, 12, 17, 19, 24, 34, 38, 51, 57, 68, 76, 102, 114, 136, 152, 204, 228, 323, 408, 456, 646, 969, 1292, 1938, 2584, 3876, 7752
The factors of 7616 are 1, 2, 4, 7, 8, 14, 16, 17, 28, 32, 34, 56, 64, 68, 112, 119, 136, 224, 238, 272, 448, 476, 544, 952, 1088, 1904, 3808, 7616
The HCF of 7752,7616 is 136.
Lets's calculate GCF of 7752,7616
| 2 | 7752, 7616 |
| 2 | 3876, 3808 |
| 2 | 1938, 1904 |
| 17 | 969, 952 |
| 57, 56 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 17 = 136
Greatest Common Factor of 7752,7616 By Matching Biggest Common Factor Method
Now, list down the factors of 7752
:1,2,3,4,6,8,12,17,19,24,34,38,51,57,68,76,102,114,136,152,204,228,323,408,456,646,969,1292,1938,2584,3876,7752
Now, list down the factors of 7616
:1,2,4,7,8,14,16,17,28,32,34,56,64,68,112,119,136,224,238,272,448,476,544,952,1088,1904,3808,7616
Greatest Common Factor
We found the factors 7752,7616 . The biggest common factor number is the GCF number.
So the greatest common factor 7752,7616 is 136.
Lets's calculate LCM of 560,814
| 2 | 560, 814 |
| 280, 407 |
∴ So the LCM of the given numbers is 2 x 280 x 407 = 227920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 136/227920
Therefore, the GCF of Fractions 7752/560,7616/814 is 136/227920
Least Common Multiple of 560,814 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 560,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(560,814) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(560,814) x common factors =2 x 1 = 2
LCM(560,814) = ( 560 × 814 ) / 2
LCM(560,814) = 455840 / 2
LCM(560,814) = 227920
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FAQs on GCF of Fractions of 7752/560, 7616/814
1. What is the HCF of 7752,7616?
The HCF of 7752,7616 is 136
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 7752/560, 7616/814?
Answer: GCF of Numerators as per given numbers 7752/560, 7616/814 is
GCF of Numerators i.e. for 7752,7616 is 136
LCM of denominators i.e. for 560,814 is 227920.
Thus, GCF of Fractions is 136/227920.Finally, GCF of Fractions for 7752/560, 7616/814 is 136/227920.