GCF of 108/152, 509/729
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 108/152, 509/729 i.e 1/110808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 108/152, 509/729.
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 108/152,509/729?
Given fractions are 108/152,509/729
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 108/152,509/729, numerators are 108,509
Denominators are 152,729
The GCF of 108,509 is 1 .
LCM of 152,729 is 110808.
The greatest common factor of 108/152,509/729 = [GCF of 108,509]/[LCM of 152,729]= 1/110808
Therefore, the GCF of 108/152,509/729 is 1/110808.
To find the highest common factor of 108,509, we have to find the factors of both numbers and list the highest common factor.
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 509 are 1, 509
The HCF of 108,509 is 1.
Lets's calculate GCF of 108,509
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 108,509 By Matching Biggest Common Factor Method
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Now, list down the factors of 509
:1,509
Greatest Common Factor
We found the factors 108,509 . The biggest common factor number is the GCF number.
So the greatest common factor 108,509 is 1.
Lets's calculate LCM of 152,729
Given numbers has no common factors except 1. So, there LCM is their product i.e 110808
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/110808
Therefore, the GCF of Fractions 108/152,509/729 is 1/110808
Least Common Multiple of 152,729 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 152,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(152,729) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(152,729) x common factors =1 x 1 = 1
LCM(152,729) = ( 152 × 729 ) / 1
LCM(152,729) = 110808 / 1
LCM(152,729) = 110808
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FAQs on GCF of Fractions of 108/152, 509/729
1. What is the HCF of 108,509?
The HCF of 108,509 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 108/152, 509/729?
Answer: GCF of Numerators as per given numbers 108/152, 509/729 is
GCF of Numerators i.e. for 108,509 is 1
LCM of denominators i.e. for 152,729 is 110808.
Thus, GCF of Fractions is 1/110808.Finally, GCF of Fractions for 108/152, 509/729 is 1/110808.