GCF of 545/14, 305/329
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 545/14, 305/329 i.e 5/658 easily. The following is the detailed procedure to determine the greatest common factor of fractions 545/14, 305/329.
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 545/14,305/329?
Given fractions are 545/14,305/329
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 545/14,305/329, numerators are 545,305
Denominators are 14,329
The GCF of 545,305 is 5 .
LCM of 14,329 is 658.
The greatest common factor of 545/14,305/329 = [GCF of 545,305]/[LCM of 14,329]= 5/658
Therefore, the GCF of 545/14,305/329 is 5/658.
To find the highest common factor of 545,305, we have to find the factors of both numbers and list the highest common factor.
The factors of 545 are 1, 5, 109, 545
The factors of 305 are 1, 5, 61, 305
The HCF of 545,305 is 5.
Lets's calculate GCF of 545,305
| 5 | 545, 305 |
| 109, 61 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 545,305 By Matching Biggest Common Factor Method
Now, list down the factors of 545
:1,5,109,545
Now, list down the factors of 305
:1,5,61,305
Greatest Common Factor
We found the factors 545,305 . The biggest common factor number is the GCF number.
So the greatest common factor 545,305 is 5.
Lets's calculate LCM of 14,329
| 7 | 14, 329 |
| 2, 47 |
∴ So the LCM of the given numbers is 7 x 2 x 47 = 658
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/658
Therefore, the GCF of Fractions 545/14,305/329 is 5/658
Least Common Multiple of 14,329 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 14,329 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,329) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(14,329) x common factors =7 x 1 = 7
LCM(14,329) = ( 14 × 329 ) / 7
LCM(14,329) = 4606 / 7
LCM(14,329) = 658
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FAQs on GCF of Fractions of 545/14, 305/329
1. What is the HCF of 545,305?
The HCF of 545,305 is 5
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 545/14, 305/329?
Answer: GCF of Numerators as per given numbers 545/14, 305/329 is
GCF of Numerators i.e. for 545,305 is 5
LCM of denominators i.e. for 14,329 is 658.
Thus, GCF of Fractions is 5/658.Finally, GCF of Fractions for 545/14, 305/329 is 5/658.