GCF of 7920/588, 4192/3170
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7920/588, 4192/3170 i.e 16/931980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7920/588, 4192/3170.
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 7920/588,4192/3170?
Given fractions are 7920/588,4192/3170
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 7920/588,4192/3170, numerators are 7920,4192
Denominators are 588,3170
The GCF of 7920,4192 is 16 .
LCM of 588,3170 is 931980.
The greatest common factor of 7920/588,4192/3170 = [GCF of 7920,4192]/[LCM of 588,3170]= 16/931980
Therefore, the GCF of 7920/588,4192/3170 is 16/931980.
To find the highest common factor of 7920,4192, we have to find the factors of both numbers and list the highest common factor.
The factors of 7920 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 48, 55, 60, 66, 72, 80, 88, 90, 99, 110, 120, 132, 144, 165, 176, 180, 198, 220, 240, 264, 330, 360, 396, 440, 495, 528, 660, 720, 792, 880, 990, 1320, 1584, 1980, 2640, 3960, 7920
The factors of 4192 are 1, 2, 4, 8, 16, 32, 131, 262, 524, 1048, 2096, 4192
The HCF of 7920,4192 is 16.
Lets's calculate GCF of 7920,4192
| 2 | 7920, 4192 |
| 2 | 3960, 2096 |
| 2 | 1980, 1048 |
| 2 | 990, 524 |
| 495, 262 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 7920,4192 By Matching Biggest Common Factor Method
Now, list down the factors of 7920
:1,2,3,4,5,6,8,9,10,11,12,15,16,18,20,22,24,30,33,36,40,44,45,48,55,60,66,72,80,88,90,99,110,120,132,144,165,176,180,198,220,240,264,330,360,396,440,495,528,660,720,792,880,990,1320,1584,1980,2640,3960,7920
Now, list down the factors of 4192
:1,2,4,8,16,32,131,262,524,1048,2096,4192
Greatest Common Factor
We found the factors 7920,4192 . The biggest common factor number is the GCF number.
So the greatest common factor 7920,4192 is 16.
Lets's calculate LCM of 588,3170
| 2 | 588, 3170 |
| 294, 1585 |
∴ So the LCM of the given numbers is 2 x 294 x 1585 = 931980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/931980
Therefore, the GCF of Fractions 7920/588,4192/3170 is 16/931980
Least Common Multiple of 588,3170 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 588,3170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(588,3170) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(588,3170) x common factors =2 x 1 = 2
LCM(588,3170) = ( 588 × 3170 ) / 2
LCM(588,3170) = 1863960 / 2
LCM(588,3170) = 931980
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FAQs on GCF of Fractions of 7920/588, 4192/3170
1. What is the HCF of 7920,4192?
The HCF of 7920,4192 is 16
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 7920/588, 4192/3170?
Answer: GCF of Numerators as per given numbers 7920/588, 4192/3170 is
GCF of Numerators i.e. for 7920,4192 is 16
LCM of denominators i.e. for 588,3170 is 931980.
Thus, GCF of Fractions is 16/931980.Finally, GCF of Fractions for 7920/588, 4192/3170 is 16/931980.