GCF of 464/109, 6816/709
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 464/109, 6816/709 i.e 16/77281 easily. The following is the detailed procedure to determine the greatest common factor of fractions 464/109, 6816/709.
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 464/109,6816/709?
Given fractions are 464/109,6816/709
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 464/109,6816/709, numerators are 464,6816
Denominators are 109,709
The GCF of 464,6816 is 16 .
LCM of 109,709 is 77281.
The greatest common factor of 464/109,6816/709 = [GCF of 464,6816]/[LCM of 109,709]= 16/77281
Therefore, the GCF of 464/109,6816/709 is 16/77281.
To find the highest common factor of 464,6816, we have to find the factors of both numbers and list the highest common factor.
The factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, 464
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 HCF of 464,6816 is 16.
Lets's calculate GCF of 464,6816
| 2 | 464, 6816 |
| 2 | 232, 3408 |
| 2 | 116, 1704 |
| 2 | 58, 852 |
| 29, 426 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 464,6816 By Matching Biggest Common Factor Method
Now, list down the factors of 464
:1,2,4,8,16,29,58,116,232,464
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
Greatest Common Factor
We found the factors 464,6816 . The biggest common factor number is the GCF number.
So the greatest common factor 464,6816 is 16.
Lets's calculate LCM of 109,709
Given numbers has no common factors except 1. So, there LCM is their product i.e 77281
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/77281
Therefore, the GCF of Fractions 464/109,6816/709 is 16/77281
Least Common Multiple of 109,709 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 109,709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(109,709) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(109,709) x common factors =1 x 1 = 1
LCM(109,709) = ( 109 × 709 ) / 1
LCM(109,709) = 77281 / 1
LCM(109,709) = 77281
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FAQs on GCF of Fractions of 464/109, 6816/709
1. What is the HCF of 464,6816?
The HCF of 464,6816 is 16
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 464/109, 6816/709?
Answer: GCF of Numerators as per given numbers 464/109, 6816/709 is
GCF of Numerators i.e. for 464,6816 is 16
LCM of denominators i.e. for 109,709 is 77281.
Thus, GCF of Fractions is 16/77281.Finally, GCF of Fractions for 464/109, 6816/709 is 16/77281.