GCF of 6816/561, 1755/774
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6816/561, 1755/774 i.e 3/144738 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6816/561, 1755/774.
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 6816/561,1755/774?
Given fractions are 6816/561,1755/774
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 6816/561,1755/774, numerators are 6816,1755
Denominators are 561,774
The GCF of 6816,1755 is 3 .
LCM of 561,774 is 144738.
The greatest common factor of 6816/561,1755/774 = [GCF of 6816,1755]/[LCM of 561,774]= 3/144738
Therefore, the GCF of 6816/561,1755/774 is 3/144738.
To find the highest common factor of 6816,1755, we have to find the factors of both numbers and list the highest common factor.
The factors of 6816 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 71, 96, 142, 213, 284, 426, 568, 852, 1136, 1704, 2272, 3408, 6816
The factors of 1755 are 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755
The HCF of 6816,1755 is 3.
Lets's calculate GCF of 6816,1755
| 3 | 6816, 1755 |
| 2272, 585 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 6816,1755 By Matching Biggest Common Factor Method
Now, list down the factors of 6816
:1,2,3,4,6,8,12,16,24,32,48,71,96,142,213,284,426,568,852,1136,1704,2272,3408,6816
Now, list down the factors of 1755
:1,3,5,9,13,15,27,39,45,65,117,135,195,351,585,1755
Greatest Common Factor
We found the factors 6816,1755 . The biggest common factor number is the GCF number.
So the greatest common factor 6816,1755 is 3.
Lets's calculate LCM of 561,774
| 3 | 561, 774 |
| 187, 258 |
∴ So the LCM of the given numbers is 3 x 187 x 258 = 144738
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/144738
Therefore, the GCF of Fractions 6816/561,1755/774 is 3/144738
Least Common Multiple of 561,774 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 561,774 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(561,774) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(561,774) x common factors =3 x 1 = 3
LCM(561,774) = ( 561 × 774 ) / 3
LCM(561,774) = 434214 / 3
LCM(561,774) = 144738
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FAQs on GCF of Fractions of 6816/561, 1755/774
1. What is the HCF of 6816,1755?
The HCF of 6816,1755 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 6816/561, 1755/774?
Answer: GCF of Numerators as per given numbers 6816/561, 1755/774 is
GCF of Numerators i.e. for 6816,1755 is 3
LCM of denominators i.e. for 561,774 is 144738.
Thus, GCF of Fractions is 3/144738.Finally, GCF of Fractions for 6816/561, 1755/774 is 3/144738.