GCF of 299/409, 105/586
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 299/409, 105/586 i.e 1/239674 easily. The following is the detailed procedure to determine the greatest common factor of fractions 299/409, 105/586.
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 299/409,105/586?
Given fractions are 299/409,105/586
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 299/409,105/586, numerators are 299,105
Denominators are 409,586
The GCF of 299,105 is 1 .
LCM of 409,586 is 239674.
The greatest common factor of 299/409,105/586 = [GCF of 299,105]/[LCM of 409,586]= 1/239674
Therefore, the GCF of 299/409,105/586 is 1/239674.
To find the highest common factor of 299,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 299 are 1, 13, 23, 299
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 299,105 is 1.
Lets's calculate GCF of 299,105
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 299,105 By Matching Biggest Common Factor Method
Now, list down the factors of 299
:1,13,23,299
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 299,105 . The biggest common factor number is the GCF number.
So the greatest common factor 299,105 is 1.
Lets's calculate LCM of 409,586
Given numbers has no common factors except 1. So, there LCM is their product i.e 239674
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/239674
Therefore, the GCF of Fractions 299/409,105/586 is 1/239674
Least Common Multiple of 409,586 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 409,586 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,586) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,586) x common factors =1 x 1 = 1
LCM(409,586) = ( 409 × 586 ) / 1
LCM(409,586) = 239674 / 1
LCM(409,586) = 239674
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FAQs on GCF of Fractions of 299/409, 105/586
1. What is the HCF of 299,105?
The HCF of 299,105 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 299/409, 105/586?
Answer: GCF of Numerators as per given numbers 299/409, 105/586 is
GCF of Numerators i.e. for 299,105 is 1
LCM of denominators i.e. for 409,586 is 239674.
Thus, GCF of Fractions is 1/239674.Finally, GCF of Fractions for 299/409, 105/586 is 1/239674.