GCF of 288/578, 214/809
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 288/578, 214/809 i.e 2/467602 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/578, 214/809.
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 288/578,214/809?
Given fractions are 288/578,214/809
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 288/578,214/809, numerators are 288,214
Denominators are 578,809
The GCF of 288,214 is 2 .
LCM of 578,809 is 467602.
The greatest common factor of 288/578,214/809 = [GCF of 288,214]/[LCM of 578,809]= 2/467602
Therefore, the GCF of 288/578,214/809 is 2/467602.
To find the highest common factor of 288,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The factors of 214 are 1, 2, 107, 214
The HCF of 288,214 is 2.
Lets's calculate GCF of 288,214
| 2 | 288, 214 |
| 144, 107 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 288,214 By Matching Biggest Common Factor Method
Now, list down the factors of 288
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 288,214 . The biggest common factor number is the GCF number.
So the greatest common factor 288,214 is 2.
Lets's calculate LCM of 578,809
Given numbers has no common factors except 1. So, there LCM is their product i.e 467602
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/467602
Therefore, the GCF of Fractions 288/578,214/809 is 2/467602
Least Common Multiple of 578,809 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 578,809 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,809) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(578,809) x common factors =1 x 1 = 1
LCM(578,809) = ( 578 × 809 ) / 1
LCM(578,809) = 467602 / 1
LCM(578,809) = 467602
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FAQs on GCF of Fractions of 288/578, 214/809
1. What is the HCF of 288,214?
The HCF of 288,214 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 288/578, 214/809?
Answer: GCF of Numerators as per given numbers 288/578, 214/809 is
GCF of Numerators i.e. for 288,214 is 2
LCM of denominators i.e. for 578,809 is 467602.
Thus, GCF of Fractions is 2/467602.Finally, GCF of Fractions for 288/578, 214/809 is 2/467602.