GCF of 5504/680, 2560/1516
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5504/680, 2560/1516 i.e 128/257720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5504/680, 2560/1516.
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 5504/680,2560/1516?
Given fractions are 5504/680,2560/1516
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 5504/680,2560/1516, numerators are 5504,2560
Denominators are 680,1516
The GCF of 5504,2560 is 128 .
LCM of 680,1516 is 257720.
The greatest common factor of 5504/680,2560/1516 = [GCF of 5504,2560]/[LCM of 680,1516]= 128/257720
Therefore, the GCF of 5504/680,2560/1516 is 128/257720.
To find the highest common factor of 5504,2560, we have to find the factors of both numbers and list the highest common factor.
The factors of 5504 are 1, 2, 4, 8, 16, 32, 43, 64, 86, 128, 172, 344, 688, 1376, 2752, 5504
The factors of 2560 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1280, 2560
The HCF of 5504,2560 is 128.
Lets's calculate GCF of 5504,2560
| 2 | 5504, 2560 |
| 2 | 2752, 1280 |
| 2 | 1376, 640 |
| 2 | 688, 320 |
| 2 | 344, 160 |
| 2 | 172, 80 |
| 2 | 86, 40 |
| 43, 20 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128
Greatest Common Factor of 5504,2560 By Matching Biggest Common Factor Method
Now, list down the factors of 5504
:1,2,4,8,16,32,43,64,86,128,172,344,688,1376,2752,5504
Now, list down the factors of 2560
:1,2,4,5,8,10,16,20,32,40,64,80,128,160,256,320,512,640,1280,2560
Greatest Common Factor
We found the factors 5504,2560 . The biggest common factor number is the GCF number.
So the greatest common factor 5504,2560 is 128.
Lets's calculate LCM of 680,1516
| 2 | 680, 1516 |
| 2 | 340, 758 |
| 170, 379 |
∴ So the LCM of the given numbers is 2 x 2 x 170 x 379 = 257720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 128/257720
Therefore, the GCF of Fractions 5504/680,2560/1516 is 128/257720
Least Common Multiple of 680,1516 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 680,1516 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(680,1516) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(680,1516) x common factors =4 x 1 = 4
LCM(680,1516) = ( 680 × 1516 ) / 4
LCM(680,1516) = 1030880 / 4
LCM(680,1516) = 257720
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FAQs on GCF of Fractions of 5504/680, 2560/1516
1. What is the HCF of 5504,2560?
The HCF of 5504,2560 is 128
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 5504/680, 2560/1516?
Answer: GCF of Numerators as per given numbers 5504/680, 2560/1516 is
GCF of Numerators i.e. for 5504,2560 is 128
LCM of denominators i.e. for 680,1516 is 257720.
Thus, GCF of Fractions is 128/257720.Finally, GCF of Fractions for 5504/680, 2560/1516 is 128/257720.