GCF of 430/212, 2013/320
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 430/212, 2013/320 i.e 1/16960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 430/212, 2013/320.
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 430/212,2013/320?
Given fractions are 430/212,2013/320
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 430/212,2013/320, numerators are 430,2013
Denominators are 212,320
The GCF of 430,2013 is 1 .
LCM of 212,320 is 16960.
The greatest common factor of 430/212,2013/320 = [GCF of 430,2013]/[LCM of 212,320]= 1/16960
Therefore, the GCF of 430/212,2013/320 is 1/16960.
To find the highest common factor of 430,2013, we have to find the factors of both numbers and list the highest common factor.
The factors of 430 are 1, 2, 5, 10, 43, 86, 215, 430
The factors of 2013 are 1, 3, 11, 33, 61, 183, 671, 2013
The HCF of 430,2013 is 1.
Lets's calculate GCF of 430,2013
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 430,2013 By Matching Biggest Common Factor Method
Now, list down the factors of 430
:1,2,5,10,43,86,215,430
Now, list down the factors of 2013
:1,3,11,33,61,183,671,2013
Greatest Common Factor
We found the factors 430,2013 . The biggest common factor number is the GCF number.
So the greatest common factor 430,2013 is 1.
Lets's calculate LCM of 212,320
| 2 | 212, 320 |
| 2 | 106, 160 |
| 53, 80 |
∴ So the LCM of the given numbers is 2 x 2 x 53 x 80 = 16960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16960
Therefore, the GCF of Fractions 430/212,2013/320 is 1/16960
Least Common Multiple of 212,320 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 212,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(212,320) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(212,320) x common factors =4 x 1 = 4
LCM(212,320) = ( 212 × 320 ) / 4
LCM(212,320) = 67840 / 4
LCM(212,320) = 16960
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FAQs on GCF of Fractions of 430/212, 2013/320
1. What is the HCF of 430,2013?
The HCF of 430,2013 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 430/212, 2013/320?
Answer: GCF of Numerators as per given numbers 430/212, 2013/320 is
GCF of Numerators i.e. for 430,2013 is 1
LCM of denominators i.e. for 212,320 is 16960.
Thus, GCF of Fractions is 1/16960.Finally, GCF of Fractions for 430/212, 2013/320 is 1/16960.