GCF of 437/12, 828/7209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 437/12, 828/7209 i.e 23/28836 easily. The following is the detailed procedure to determine the greatest common factor of fractions 437/12, 828/7209.
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 437/12,828/7209?
Given fractions are 437/12,828/7209
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 437/12,828/7209, numerators are 437,828
Denominators are 12,7209
The GCF of 437,828 is 23 .
LCM of 12,7209 is 28836.
The greatest common factor of 437/12,828/7209 = [GCF of 437,828]/[LCM of 12,7209]= 23/28836
Therefore, the GCF of 437/12,828/7209 is 23/28836.
To find the highest common factor of 437,828, we have to find the factors of both numbers and list the highest common factor.
The factors of 437 are 1, 19, 23, 437
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The HCF of 437,828 is 23.
Lets's calculate GCF of 437,828
| 23 | 437, 828 |
| 19, 36 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 437,828 By Matching Biggest Common Factor Method
Now, list down the factors of 437
:1,19,23,437
Now, list down the factors of 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Greatest Common Factor
We found the factors 437,828 . The biggest common factor number is the GCF number.
So the greatest common factor 437,828 is 23.
Lets's calculate LCM of 12,7209
| 3 | 12, 7209 |
| 4, 2403 |
∴ So the LCM of the given numbers is 3 x 4 x 2403 = 28836
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/28836
Therefore, the GCF of Fractions 437/12,828/7209 is 23/28836
Least Common Multiple of 12,7209 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 12,7209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,7209) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(12,7209) x common factors =3 x 1 = 3
LCM(12,7209) = ( 12 × 7209 ) / 3
LCM(12,7209) = 86508 / 3
LCM(12,7209) = 28836
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FAQs on GCF of Fractions of 437/12, 828/7209
1. What is the HCF of 437,828?
The HCF of 437,828 is 23
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 437/12, 828/7209?
Answer: GCF of Numerators as per given numbers 437/12, 828/7209 is
GCF of Numerators i.e. for 437,828 is 23
LCM of denominators i.e. for 12,7209 is 28836.
Thus, GCF of Fractions is 23/28836.Finally, GCF of Fractions for 437/12, 828/7209 is 23/28836.