GCF of 9120/192, 5984/9467
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9120/192, 5984/9467 i.e 32/1817664 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9120/192, 5984/9467.
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 9120/192,5984/9467?
Given fractions are 9120/192,5984/9467
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 9120/192,5984/9467, numerators are 9120,5984
Denominators are 192,9467
The GCF of 9120,5984 is 32 .
LCM of 192,9467 is 1817664.
The greatest common factor of 9120/192,5984/9467 = [GCF of 9120,5984]/[LCM of 192,9467]= 32/1817664
Therefore, the GCF of 9120/192,5984/9467 is 32/1817664.
To find the highest common factor of 9120,5984, we have to find the factors of both numbers and list the highest common factor.
The factors of 9120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 76, 80, 95, 96, 114, 120, 152, 160, 190, 228, 240, 285, 304, 380, 456, 480, 570, 608, 760, 912, 1140, 1520, 1824, 2280, 3040, 4560, 9120
The factors of 5984 are 1, 2, 4, 8, 11, 16, 17, 22, 32, 34, 44, 68, 88, 136, 176, 187, 272, 352, 374, 544, 748, 1496, 2992, 5984
The HCF of 9120,5984 is 32.
Lets's calculate GCF of 9120,5984
| 2 | 9120, 5984 |
| 2 | 4560, 2992 |
| 2 | 2280, 1496 |
| 2 | 1140, 748 |
| 2 | 570, 374 |
| 285, 187 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 9120,5984 By Matching Biggest Common Factor Method
Now, list down the factors of 9120
:1,2,3,4,5,6,8,10,12,15,16,19,20,24,30,32,38,40,48,57,60,76,80,95,96,114,120,152,160,190,228,240,285,304,380,456,480,570,608,760,912,1140,1520,1824,2280,3040,4560,9120
Now, list down the factors of 5984
:1,2,4,8,11,16,17,22,32,34,44,68,88,136,176,187,272,352,374,544,748,1496,2992,5984
Greatest Common Factor
We found the factors 9120,5984 . The biggest common factor number is the GCF number.
So the greatest common factor 9120,5984 is 32.
Lets's calculate LCM of 192,9467
Given numbers has no common factors except 1. So, there LCM is their product i.e 1817664
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/1817664
Therefore, the GCF of Fractions 9120/192,5984/9467 is 32/1817664
Least Common Multiple of 192,9467 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 192,9467 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(192,9467) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(192,9467) x common factors =1 x 1 = 1
LCM(192,9467) = ( 192 × 9467 ) / 1
LCM(192,9467) = 1817664 / 1
LCM(192,9467) = 1817664
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FAQs on GCF of Fractions of 9120/192, 5984/9467
1. What is the HCF of 9120,5984?
The HCF of 9120,5984 is 32
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 9120/192, 5984/9467?
Answer: GCF of Numerators as per given numbers 9120/192, 5984/9467 is
GCF of Numerators i.e. for 9120,5984 is 32
LCM of denominators i.e. for 192,9467 is 1817664.
Thus, GCF of Fractions is 32/1817664.Finally, GCF of Fractions for 9120/192, 5984/9467 is 32/1817664.