GCF of 205/34, 768/456
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 205/34, 768/456 i.e 1/7752 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/34, 768/456.
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 205/34,768/456?
Given fractions are 205/34,768/456
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 205/34,768/456, numerators are 205,768
Denominators are 34,456
The GCF of 205,768 is 1 .
LCM of 34,456 is 7752.
The greatest common factor of 205/34,768/456 = [GCF of 205,768]/[LCM of 34,456]= 1/7752
Therefore, the GCF of 205/34,768/456 is 1/7752.
To find the highest common factor of 205,768, we have to find the factors of both numbers and list the highest common factor.
The factors of 205 are 1, 5, 41, 205
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 205,768 is 1.
Lets's calculate GCF of 205,768
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 205,768 By Matching Biggest Common Factor Method
Now, list down the factors of 205
:1,5,41,205
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 205,768 . The biggest common factor number is the GCF number.
So the greatest common factor 205,768 is 1.
Lets's calculate LCM of 34,456
| 2 | 34, 456 |
| 17, 228 |
∴ So the LCM of the given numbers is 2 x 17 x 228 = 7752
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7752
Therefore, the GCF of Fractions 205/34,768/456 is 1/7752
Least Common Multiple of 34,456 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 34,456 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,456) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,456) x common factors =2 x 1 = 2
LCM(34,456) = ( 34 × 456 ) / 2
LCM(34,456) = 15504 / 2
LCM(34,456) = 7752
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FAQs on GCF of Fractions of 205/34, 768/456
1. What is the HCF of 205,768?
The HCF of 205,768 is 1
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 205/34, 768/456?
Answer: GCF of Numerators as per given numbers 205/34, 768/456 is
GCF of Numerators i.e. for 205,768 is 1
LCM of denominators i.e. for 34,456 is 7752.
Thus, GCF of Fractions is 1/7752.Finally, GCF of Fractions for 205/34, 768/456 is 1/7752.