GCF of 17/512, 55/184, 649/320
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 17/512, 55/184, 649/320 i.e 1/58880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/512, 55/184, 649/320.
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 17/512,55/184,649/320?
Given fractions are 17/512,55/184,649/320
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 17/512,55/184,649/320, numerators are 17,55,649
Denominators are 512,184,320
The GCF of 17,55,649 is 1 .
LCM of 512,184,320 is 58880.
The greatest common factor of 17/512,55/184,649/320 = [GCF of 17,55,649]/[LCM of 512,184,320]= 1/58880
Therefore, the GCF of 17/512,55/184,649/320 is 1/58880.
To find the highest common factor of 17,55,649, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 55 are 1, 5, 11, 55
The factors of 649 are 1, 11, 59, 649
The HCF of 17,55,649 is 1.
Lets's calculate GCF of 17,55,649
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 17,55,649 By Matching Biggest Common Factor Method
Now, list down the factors of 17
:1,17
Now, list down the factors of 55
:1,5,11,55
Now, list down the factors of 649
:1,11,59,649
Greatest Common Factor
We found the factors 17,55,649 . The biggest common factor number is the GCF number.
So the greatest common factor 17,55,649 is 1.
Lets's calculate LCM of 512,184,320
| 2 | 512, 184, 320 |
| 2 | 256, 92, 160 |
| 2 | 128, 46, 80 |
| 2 | 64, 23, 40 |
| 2 | 32, 23, 20 |
| 2 | 16, 23, 10 |
| 8, 23, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 8 x 23 x 5 = 58880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/58880
Therefore, the GCF of Fractions 17/512,55/184,649/320 is 1/58880
Least Common Multiple of 512,184,320 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 512,184,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,184,320) = 8
common factors(in case of two or more numbers have common factors) = 64
GCF(512,184,320) x common factors =8 x 64 = 512
LCM(512,184,320) = ( 512 × 184 × 320 ) / 512
LCM(512,184,320) = 30146560 / 512
LCM(512,184,320) = 58880
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FAQs on GCF of Fractions of 17/512, 55/184, 649/320
1. What is the HCF of 17,55,649?
The HCF of 17,55,649 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 17/512, 55/184, 649/320?
Answer: GCF of Numerators as per given numbers 17/512, 55/184, 649/320 is
GCF of Numerators i.e. for 17,55,649 is 1
LCM of denominators i.e. for 512,184,320 is 58880.
Thus, GCF of Fractions is 1/58880.Finally, GCF of Fractions for 17/512, 55/184, 649/320 is 1/58880.