GCF of 240/260, 514/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 240/260, 514/414 i.e 2/53820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 240/260, 514/414.
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 240/260,514/414?
Given fractions are 240/260,514/414
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 240/260,514/414, numerators are 240,514
Denominators are 260,414
The GCF of 240,514 is 2 .
LCM of 260,414 is 53820.
The greatest common factor of 240/260,514/414 = [GCF of 240,514]/[LCM of 260,414]= 2/53820
Therefore, the GCF of 240/260,514/414 is 2/53820.
To find the highest common factor of 240,514, we have to find the factors of both numbers and list the highest common factor.
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
The factors of 514 are 1, 2, 257, 514
The HCF of 240,514 is 2.
Lets's calculate GCF of 240,514
| 2 | 240, 514 |
| 120, 257 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 240,514 By Matching Biggest Common Factor Method
Now, list down the factors of 240
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240
Now, list down the factors of 514
:1,2,257,514
Greatest Common Factor
We found the factors 240,514 . The biggest common factor number is the GCF number.
So the greatest common factor 240,514 is 2.
Lets's calculate LCM of 260,414
| 2 | 260, 414 |
| 130, 207 |
∴ So the LCM of the given numbers is 2 x 130 x 207 = 53820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/53820
Therefore, the GCF of Fractions 240/260,514/414 is 2/53820
Least Common Multiple of 260,414 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 260,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(260,414) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(260,414) x common factors =2 x 1 = 2
LCM(260,414) = ( 260 × 414 ) / 2
LCM(260,414) = 107640 / 2
LCM(260,414) = 53820
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FAQs on GCF of Fractions of 240/260, 514/414
1. What is the HCF of 240,514?
The HCF of 240,514 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 240/260, 514/414?
Answer: GCF of Numerators as per given numbers 240/260, 514/414 is
GCF of Numerators i.e. for 240,514 is 2
LCM of denominators i.e. for 260,414 is 53820.
Thus, GCF of Fractions is 2/53820.Finally, GCF of Fractions for 240/260, 514/414 is 2/53820.