GCF of 909/14, 286/7754
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 909/14, 286/7754 i.e 1/54278 easily. The following is the detailed procedure to determine the greatest common factor of fractions 909/14, 286/7754.
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 909/14,286/7754?
Given fractions are 909/14,286/7754
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 909/14,286/7754, numerators are 909,286
Denominators are 14,7754
The GCF of 909,286 is 1 .
LCM of 14,7754 is 54278.
The greatest common factor of 909/14,286/7754 = [GCF of 909,286]/[LCM of 14,7754]= 1/54278
Therefore, the GCF of 909/14,286/7754 is 1/54278.
To find the highest common factor of 909,286, we have to find the factors of both numbers and list the highest common factor.
The factors of 909 are 1, 3, 9, 101, 303, 909
The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286
The HCF of 909,286 is 1.
Lets's calculate GCF of 909,286
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 909,286 By Matching Biggest Common Factor Method
Now, list down the factors of 909
:1,3,9,101,303,909
Now, list down the factors of 286
:1,2,11,13,22,26,143,286
Greatest Common Factor
We found the factors 909,286 . The biggest common factor number is the GCF number.
So the greatest common factor 909,286 is 1.
Lets's calculate LCM of 14,7754
| 2 | 14, 7754 |
| 7, 3877 |
∴ So the LCM of the given numbers is 2 x 7 x 3877 = 54278
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/54278
Therefore, the GCF of Fractions 909/14,286/7754 is 1/54278
Least Common Multiple of 14,7754 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 14,7754 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,7754) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(14,7754) x common factors =2 x 1 = 2
LCM(14,7754) = ( 14 × 7754 ) / 2
LCM(14,7754) = 108556 / 2
LCM(14,7754) = 54278
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FAQs on GCF of Fractions of 909/14, 286/7754
1. What is the HCF of 909,286?
The HCF of 909,286 is 1
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 909/14, 286/7754?
Answer: GCF of Numerators as per given numbers 909/14, 286/7754 is
GCF of Numerators i.e. for 909,286 is 1
LCM of denominators i.e. for 14,7754 is 54278.
Thus, GCF of Fractions is 1/54278.Finally, GCF of Fractions for 909/14, 286/7754 is 1/54278.