GCF of 290/13, 319/478
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 290/13, 319/478 i.e 29/6214 easily. The following is the detailed procedure to determine the greatest common factor of fractions 290/13, 319/478.
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 290/13,319/478?
Given fractions are 290/13,319/478
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 290/13,319/478, numerators are 290,319
Denominators are 13,478
The GCF of 290,319 is 29 .
LCM of 13,478 is 6214.
The greatest common factor of 290/13,319/478 = [GCF of 290,319]/[LCM of 13,478]= 29/6214
Therefore, the GCF of 290/13,319/478 is 29/6214.
To find the highest common factor of 290,319, we have to find the factors of both numbers and list the highest common factor.
The factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290
The factors of 319 are 1, 11, 29, 319
The HCF of 290,319 is 29.
Lets's calculate GCF of 290,319
| 29 | 290, 319 |
| 10, 11 |
∴ So the GCF of the given numbers is 29 = 29
Greatest Common Factor of 290,319 By Matching Biggest Common Factor Method
Now, list down the factors of 290
:1,2,5,10,29,58,145,290
Now, list down the factors of 319
:1,11,29,319
Greatest Common Factor
We found the factors 290,319 . The biggest common factor number is the GCF number.
So the greatest common factor 290,319 is 29.
Lets's calculate LCM of 13,478
Given numbers has no common factors except 1. So, there LCM is their product i.e 6214
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 29/6214
Therefore, the GCF of Fractions 290/13,319/478 is 29/6214
Least Common Multiple of 13,478 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 13,478 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,478) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(13,478) x common factors =1 x 1 = 1
LCM(13,478) = ( 13 × 478 ) / 1
LCM(13,478) = 6214 / 1
LCM(13,478) = 6214
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 290/13, 319/478
1. What is the HCF of 290,319?
The HCF of 290,319 is 29
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 290/13, 319/478?
Answer: GCF of Numerators as per given numbers 290/13, 319/478 is
GCF of Numerators i.e. for 290,319 is 29
LCM of denominators i.e. for 13,478 is 6214.
Thus, GCF of Fractions is 29/6214.Finally, GCF of Fractions for 290/13, 319/478 is 29/6214.