GCF of 3584/764, 7264/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3584/764, 7264/209 i.e 32/159676 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3584/764, 7264/209.
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 3584/764,7264/209?
Given fractions are 3584/764,7264/209
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 3584/764,7264/209, numerators are 3584,7264
Denominators are 764,209
The GCF of 3584,7264 is 32 .
LCM of 764,209 is 159676.
The greatest common factor of 3584/764,7264/209 = [GCF of 3584,7264]/[LCM of 764,209]= 32/159676
Therefore, the GCF of 3584/764,7264/209 is 32/159676.
To find the highest common factor of 3584,7264, we have to find the factors of both numbers and list the highest common factor.
The factors of 3584 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584
The factors of 7264 are 1, 2, 4, 8, 16, 32, 227, 454, 908, 1816, 3632, 7264
The HCF of 3584,7264 is 32.
Lets's calculate GCF of 3584,7264
| 2 | 3584, 7264 |
| 2 | 1792, 3632 |
| 2 | 896, 1816 |
| 2 | 448, 908 |
| 2 | 224, 454 |
| 112, 227 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 3584,7264 By Matching Biggest Common Factor Method
Now, list down the factors of 3584
:1,2,4,7,8,14,16,28,32,56,64,112,128,224,256,448,512,896,1792,3584
Now, list down the factors of 7264
:1,2,4,8,16,32,227,454,908,1816,3632,7264
Greatest Common Factor
We found the factors 3584,7264 . The biggest common factor number is the GCF number.
So the greatest common factor 3584,7264 is 32.
Lets's calculate LCM of 764,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 159676
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/159676
Therefore, the GCF of Fractions 3584/764,7264/209 is 32/159676
Least Common Multiple of 764,209 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 764,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(764,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(764,209) x common factors =1 x 1 = 1
LCM(764,209) = ( 764 × 209 ) / 1
LCM(764,209) = 159676 / 1
LCM(764,209) = 159676
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FAQs on GCF of Fractions of 3584/764, 7264/209
1. What is the HCF of 3584,7264?
The HCF of 3584,7264 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 3584/764, 7264/209?
Answer: GCF of Numerators as per given numbers 3584/764, 7264/209 is
GCF of Numerators i.e. for 3584,7264 is 32
LCM of denominators i.e. for 764,209 is 159676.
Thus, GCF of Fractions is 32/159676.Finally, GCF of Fractions for 3584/764, 7264/209 is 32/159676.