GCF of 489/73, 105/109
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 489/73, 105/109 i.e 3/7957 easily. The following is the detailed procedure to determine the greatest common factor of fractions 489/73, 105/109.
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 489/73,105/109?
Given fractions are 489/73,105/109
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 489/73,105/109, numerators are 489,105
Denominators are 73,109
The GCF of 489,105 is 3 .
LCM of 73,109 is 7957.
The greatest common factor of 489/73,105/109 = [GCF of 489,105]/[LCM of 73,109]= 3/7957
Therefore, the GCF of 489/73,105/109 is 3/7957.
To find the highest common factor of 489,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 489 are 1, 3, 163, 489
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 489,105 is 3.
Lets's calculate GCF of 489,105
| 3 | 489, 105 |
| 163, 35 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 489,105 By Matching Biggest Common Factor Method
Now, list down the factors of 489
:1,3,163,489
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 489,105 . The biggest common factor number is the GCF number.
So the greatest common factor 489,105 is 3.
Lets's calculate LCM of 73,109
Given numbers has no common factors except 1. So, there LCM is their product i.e 7957
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/7957
Therefore, the GCF of Fractions 489/73,105/109 is 3/7957
Least Common Multiple of 73,109 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 73,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(73,109) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(73,109) x common factors =1 x 1 = 1
LCM(73,109) = ( 73 × 109 ) / 1
LCM(73,109) = 7957 / 1
LCM(73,109) = 7957
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FAQs on GCF of Fractions of 489/73, 105/109
1. What is the HCF of 489,105?
The HCF of 489,105 is 3
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 489/73, 105/109?
Answer: GCF of Numerators as per given numbers 489/73, 105/109 is
GCF of Numerators i.e. for 489,105 is 3
LCM of denominators i.e. for 73,109 is 7957.
Thus, GCF of Fractions is 3/7957.Finally, GCF of Fractions for 489/73, 105/109 is 3/7957.