GCF of 3104/310, 1584/6688
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3104/310, 1584/6688 i.e 16/1036640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3104/310, 1584/6688.
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 3104/310,1584/6688?
Given fractions are 3104/310,1584/6688
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 3104/310,1584/6688, numerators are 3104,1584
Denominators are 310,6688
The GCF of 3104,1584 is 16 .
LCM of 310,6688 is 1036640.
The greatest common factor of 3104/310,1584/6688 = [GCF of 3104,1584]/[LCM of 310,6688]= 16/1036640
Therefore, the GCF of 3104/310,1584/6688 is 16/1036640.
To find the highest common factor of 3104,1584, we have to find the factors of both numbers and list the highest common factor.
The factors of 3104 are 1, 2, 4, 8, 16, 32, 97, 194, 388, 776, 1552, 3104
The factors of 1584 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 132, 144, 176, 198, 264, 396, 528, 792, 1584
The HCF of 3104,1584 is 16.
Lets's calculate GCF of 3104,1584
| 2 | 3104, 1584 |
| 2 | 1552, 792 |
| 2 | 776, 396 |
| 2 | 388, 198 |
| 194, 99 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 3104,1584 By Matching Biggest Common Factor Method
Now, list down the factors of 3104
:1,2,4,8,16,32,97,194,388,776,1552,3104
Now, list down the factors of 1584
:1,2,3,4,6,8,9,11,12,16,18,22,24,33,36,44,48,66,72,88,99,132,144,176,198,264,396,528,792,1584
Greatest Common Factor
We found the factors 3104,1584 . The biggest common factor number is the GCF number.
So the greatest common factor 3104,1584 is 16.
Lets's calculate LCM of 310,6688
| 2 | 310, 6688 |
| 155, 3344 |
∴ So the LCM of the given numbers is 2 x 155 x 3344 = 1036640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/1036640
Therefore, the GCF of Fractions 3104/310,1584/6688 is 16/1036640
Least Common Multiple of 310,6688 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 310,6688 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(310,6688) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(310,6688) x common factors =2 x 1 = 2
LCM(310,6688) = ( 310 × 6688 ) / 2
LCM(310,6688) = 2073280 / 2
LCM(310,6688) = 1036640
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 3104/310, 1584/6688
1. What is the HCF of 3104,1584?
The HCF of 3104,1584 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 3104/310, 1584/6688?
Answer: GCF of Numerators as per given numbers 3104/310, 1584/6688 is
GCF of Numerators i.e. for 3104,1584 is 16
LCM of denominators i.e. for 310,6688 is 1036640.
Thus, GCF of Fractions is 16/1036640.Finally, GCF of Fractions for 3104/310, 1584/6688 is 16/1036640.