GCF of 723/32, 768/205
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 723/32, 768/205 i.e 3/6560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 723/32, 768/205.
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 723/32,768/205?
Given fractions are 723/32,768/205
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 723/32,768/205, numerators are 723,768
Denominators are 32,205
The GCF of 723,768 is 3 .
LCM of 32,205 is 6560.
The greatest common factor of 723/32,768/205 = [GCF of 723,768]/[LCM of 32,205]= 3/6560
Therefore, the GCF of 723/32,768/205 is 3/6560.
To find the highest common factor of 723,768, we have to find the factors of both numbers and list the highest common factor.
The factors of 723 are 1, 3, 241, 723
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The HCF of 723,768 is 3.
Lets's calculate GCF of 723,768
| 3 | 723, 768 |
| 241, 256 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 723,768 By Matching Biggest Common Factor Method
Now, list down the factors of 723
:1,3,241,723
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Greatest Common Factor
We found the factors 723,768 . The biggest common factor number is the GCF number.
So the greatest common factor 723,768 is 3.
Lets's calculate LCM of 32,205
Given numbers has no common factors except 1. So, there LCM is their product i.e 6560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/6560
Therefore, the GCF of Fractions 723/32,768/205 is 3/6560
Least Common Multiple of 32,205 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 32,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,205) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(32,205) x common factors =1 x 1 = 1
LCM(32,205) = ( 32 × 205 ) / 1
LCM(32,205) = 6560 / 1
LCM(32,205) = 6560
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FAQs on GCF of Fractions of 723/32, 768/205
1. What is the HCF of 723,768?
The HCF of 723,768 is 3
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 723/32, 768/205?
Answer: GCF of Numerators as per given numbers 723/32, 768/205 is
GCF of Numerators i.e. for 723,768 is 3
LCM of denominators i.e. for 32,205 is 6560.
Thus, GCF of Fractions is 3/6560.Finally, GCF of Fractions for 723/32, 768/205 is 3/6560.