GCF of 409/13, 564/118
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 409/13, 564/118 i.e 1/1534 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/13, 564/118.
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 409/13,564/118?
Given fractions are 409/13,564/118
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 409/13,564/118, numerators are 409,564
Denominators are 13,118
The GCF of 409,564 is 1 .
LCM of 13,118 is 1534.
The greatest common factor of 409/13,564/118 = [GCF of 409,564]/[LCM of 13,118]= 1/1534
Therefore, the GCF of 409/13,564/118 is 1/1534.
To find the highest common factor of 409,564, we have to find the factors of both numbers and list the highest common factor.
The factors of 409 are 1, 409
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The HCF of 409,564 is 1.
Lets's calculate GCF of 409,564
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 409,564 By Matching Biggest Common Factor Method
Now, list down the factors of 409
:1,409
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Greatest Common Factor
We found the factors 409,564 . The biggest common factor number is the GCF number.
So the greatest common factor 409,564 is 1.
Lets's calculate LCM of 13,118
Given numbers has no common factors except 1. So, there LCM is their product i.e 1534
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1534
Therefore, the GCF of Fractions 409/13,564/118 is 1/1534
Least Common Multiple of 13,118 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 13,118 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,118) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(13,118) x common factors =1 x 1 = 1
LCM(13,118) = ( 13 × 118 ) / 1
LCM(13,118) = 1534 / 1
LCM(13,118) = 1534
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FAQs on GCF of Fractions of 409/13, 564/118
1. What is the HCF of 409,564?
The HCF of 409,564 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 409/13, 564/118?
Answer: GCF of Numerators as per given numbers 409/13, 564/118 is
GCF of Numerators i.e. for 409,564 is 1
LCM of denominators i.e. for 13,118 is 1534.
Thus, GCF of Fractions is 1/1534.Finally, GCF of Fractions for 409/13, 564/118 is 1/1534.