GCF of 3200/756, 2656/1716
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3200/756, 2656/1716 i.e 32/108108 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3200/756, 2656/1716.
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 3200/756,2656/1716?
Given fractions are 3200/756,2656/1716
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 3200/756,2656/1716, numerators are 3200,2656
Denominators are 756,1716
The GCF of 3200,2656 is 32 .
LCM of 756,1716 is 108108.
The greatest common factor of 3200/756,2656/1716 = [GCF of 3200,2656]/[LCM of 756,1716]= 32/108108
Therefore, the GCF of 3200/756,2656/1716 is 32/108108.
To find the highest common factor of 3200,2656, we have to find the factors of both numbers and list the highest common factor.
The factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200
The factors of 2656 are 1, 2, 4, 8, 16, 32, 83, 166, 332, 664, 1328, 2656
The HCF of 3200,2656 is 32.
Lets's calculate GCF of 3200,2656
| 2 | 3200, 2656 |
| 2 | 1600, 1328 |
| 2 | 800, 664 |
| 2 | 400, 332 |
| 2 | 200, 166 |
| 100, 83 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 3200,2656 By Matching Biggest Common Factor Method
Now, list down the factors of 3200
:1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,128,160,200,320,400,640,800,1600,3200
Now, list down the factors of 2656
:1,2,4,8,16,32,83,166,332,664,1328,2656
Greatest Common Factor
We found the factors 3200,2656 . The biggest common factor number is the GCF number.
So the greatest common factor 3200,2656 is 32.
Lets's calculate LCM of 756,1716
| 2 | 756, 1716 |
| 2 | 378, 858 |
| 3 | 189, 429 |
| 63, 143 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 63 x 143 = 108108
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/108108
Therefore, the GCF of Fractions 3200/756,2656/1716 is 32/108108
Least Common Multiple of 756,1716 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 756,1716 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(756,1716) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(756,1716) x common factors =12 x 1 = 12
LCM(756,1716) = ( 756 × 1716 ) / 12
LCM(756,1716) = 1297296 / 12
LCM(756,1716) = 108108
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FAQs on GCF of Fractions of 3200/756, 2656/1716
1. What is the HCF of 3200,2656?
The HCF of 3200,2656 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 3200/756, 2656/1716?
Answer: GCF of Numerators as per given numbers 3200/756, 2656/1716 is
GCF of Numerators i.e. for 3200,2656 is 32
LCM of denominators i.e. for 756,1716 is 108108.
Thus, GCF of Fractions is 32/108108.Finally, GCF of Fractions for 3200/756, 2656/1716 is 32/108108.