GCF of 513/140, 169/145
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 513/140, 169/145 i.e 1/4060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 513/140, 169/145.
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 513/140,169/145?
Given fractions are 513/140,169/145
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 513/140,169/145, numerators are 513,169
Denominators are 140,145
The GCF of 513,169 is 1 .
LCM of 140,145 is 4060.
The greatest common factor of 513/140,169/145 = [GCF of 513,169]/[LCM of 140,145]= 1/4060
Therefore, the GCF of 513/140,169/145 is 1/4060.
To find the highest common factor of 513,169, we have to find the factors of both numbers and list the highest common factor.
The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513
The factors of 169 are 1, 13, 169
The HCF of 513,169 is 1.
Lets's calculate GCF of 513,169
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 513,169 By Matching Biggest Common Factor Method
Now, list down the factors of 513
:1,3,9,19,27,57,171,513
Now, list down the factors of 169
:1,13,169
Greatest Common Factor
We found the factors 513,169 . The biggest common factor number is the GCF number.
So the greatest common factor 513,169 is 1.
Lets's calculate LCM of 140,145
| 5 | 140, 145 |
| 28, 29 |
∴ So the LCM of the given numbers is 5 x 28 x 29 = 4060
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4060
Therefore, the GCF of Fractions 513/140,169/145 is 1/4060
Least Common Multiple of 140,145 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 140,145 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(140,145) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(140,145) x common factors =5 x 1 = 5
LCM(140,145) = ( 140 × 145 ) / 5
LCM(140,145) = 20300 / 5
LCM(140,145) = 4060
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FAQs on GCF of Fractions of 513/140, 169/145
1. What is the HCF of 513,169?
The HCF of 513,169 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 513/140, 169/145?
Answer: GCF of Numerators as per given numbers 513/140, 169/145 is
GCF of Numerators i.e. for 513,169 is 1
LCM of denominators i.e. for 140,145 is 4060.
Thus, GCF of Fractions is 1/4060.Finally, GCF of Fractions for 513/140, 169/145 is 1/4060.