GCF of 260/20, 344/30, 456/12
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 260/20, 344/30, 456/12 i.e 4/60 easily. The following is the detailed procedure to determine the greatest common factor of fractions 260/20, 344/30, 456/12.
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 260/20,344/30,456/12?
Given fractions are 260/20,344/30,456/12
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 260/20,344/30,456/12, numerators are 260,344,456
Denominators are 20,30,12
The GCF of 260,344,456 is 4 .
LCM of 20,30,12 is 60.
The greatest common factor of 260/20,344/30,456/12 = [GCF of 260,344,456]/[LCM of 20,30,12]= 4/60
Therefore, the GCF of 260/20,344/30,456/12 is 4/60.
To find the highest common factor of 260,344,456, we have to find the factors of both numbers and list the highest common factor.
The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260
The factors of 344 are 1, 2, 4, 8, 43, 86, 172, 344
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 260,344,456 is 4.
Lets's calculate GCF of 260,344,456
| 2 | 260, 344, 456 |
| 2 | 130, 172, 228 |
| 65, 86, 114 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 260,344,456 By Matching Biggest Common Factor Method
Now, list down the factors of 260
:1,2,4,5,10,13,20,26,52,65,130,260
Now, list down the factors of 344
:1,2,4,8,43,86,172,344
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 260,344,456 . The biggest common factor number is the GCF number.
So the greatest common factor 260,344,456 is 4.
Lets's calculate LCM of 20,30,12
| 2 | 20, 30, 12 |
| 2 | 10, 15, 6 |
| 3 | 5, 15, 3 |
| 5 | 5, 5, 1 |
| 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 1 x 1 = 60
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/60
Therefore, the GCF of Fractions 260/20,344/30,456/12 is 4/60
Least Common Multiple of 20,30,12 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 20,30,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,30,12) = 2
common factors(in case of two or more numbers have common factors) = 60
GCF(20,30,12) x common factors =2 x 60 = 120
LCM(20,30,12) = ( 20 × 30 × 12 ) / 120
LCM(20,30,12) = 7200 / 120
LCM(20,30,12) = 60
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FAQs on GCF of Fractions of 260/20, 344/30, 456/12
1. What is the HCF of 260,344,456?
The HCF of 260,344,456 is 4
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 260/20, 344/30, 456/12?
Answer: GCF of Numerators as per given numbers 260/20, 344/30, 456/12 is
GCF of Numerators i.e. for 260,344,456 is 4
LCM of denominators i.e. for 20,30,12 is 60.
Thus, GCF of Fractions is 4/60.Finally, GCF of Fractions for 260/20, 344/30, 456/12 is 4/60.