GCF of 434/14, 580/2198
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 434/14, 580/2198 i.e 2/2198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 434/14, 580/2198.
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 434/14,580/2198?
Given fractions are 434/14,580/2198
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 434/14,580/2198, numerators are 434,580
Denominators are 14,2198
The GCF of 434,580 is 2 .
LCM of 14,2198 is 2198.
The greatest common factor of 434/14,580/2198 = [GCF of 434,580]/[LCM of 14,2198]= 2/2198
Therefore, the GCF of 434/14,580/2198 is 2/2198.
To find the highest common factor of 434,580, we have to find the factors of both numbers and list the highest common factor.
The factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The HCF of 434,580 is 2.
Lets's calculate GCF of 434,580
| 2 | 434, 580 |
| 217, 290 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 434,580 By Matching Biggest Common Factor Method
Now, list down the factors of 434
:1,2,7,14,31,62,217,434
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Greatest Common Factor
We found the factors 434,580 . The biggest common factor number is the GCF number.
So the greatest common factor 434,580 is 2.
Lets's calculate LCM of 14,2198
| 2 | 14, 2198 |
| 7 | 7, 1099 |
| 1, 157 |
∴ So the LCM of the given numbers is 2 x 7 x 1 x 157 = 2198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2198
Therefore, the GCF of Fractions 434/14,580/2198 is 2/2198
Least Common Multiple of 14,2198 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 14,2198 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,2198) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(14,2198) x common factors =14 x 1 = 14
LCM(14,2198) = ( 14 × 2198 ) / 14
LCM(14,2198) = 30772 / 14
LCM(14,2198) = 2198
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FAQs on GCF of Fractions of 434/14, 580/2198
1. What is the HCF of 434,580?
The HCF of 434,580 is 2
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 434/14, 580/2198?
Answer: GCF of Numerators as per given numbers 434/14, 580/2198 is
GCF of Numerators i.e. for 434,580 is 2
LCM of denominators i.e. for 14,2198 is 2198.
Thus, GCF of Fractions is 2/2198.Finally, GCF of Fractions for 434/14, 580/2198 is 2/2198.