GCF of 330/461, 138/170
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 330/461, 138/170 i.e 6/78370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 330/461, 138/170.
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 330/461,138/170?
Given fractions are 330/461,138/170
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 330/461,138/170, numerators are 330,138
Denominators are 461,170
The GCF of 330,138 is 6 .
LCM of 461,170 is 78370.
The greatest common factor of 330/461,138/170 = [GCF of 330,138]/[LCM of 461,170]= 6/78370
Therefore, the GCF of 330/461,138/170 is 6/78370.
To find the highest common factor of 330,138, we have to find the factors of both numbers and list the highest common factor.
The factors of 330 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The HCF of 330,138 is 6.
Lets's calculate GCF of 330,138
| 2 | 330, 138 |
| 3 | 165, 69 |
| 55, 23 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 330,138 By Matching Biggest Common Factor Method
Now, list down the factors of 330
:1,2,3,5,6,10,11,15,22,30,33,55,66,110,165,330
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 330,138 . The biggest common factor number is the GCF number.
So the greatest common factor 330,138 is 6.
Lets's calculate LCM of 461,170
Given numbers has no common factors except 1. So, there LCM is their product i.e 78370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/78370
Therefore, the GCF of Fractions 330/461,138/170 is 6/78370
Least Common Multiple of 461,170 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 461,170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(461,170) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(461,170) x common factors =1 x 1 = 1
LCM(461,170) = ( 461 × 170 ) / 1
LCM(461,170) = 78370 / 1
LCM(461,170) = 78370
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FAQs on GCF of Fractions of 330/461, 138/170
1. What is the HCF of 330,138?
The HCF of 330,138 is 6
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 330/461, 138/170?
Answer: GCF of Numerators as per given numbers 330/461, 138/170 is
GCF of Numerators i.e. for 330,138 is 6
LCM of denominators i.e. for 461,170 is 78370.
Thus, GCF of Fractions is 6/78370.Finally, GCF of Fractions for 330/461, 138/170 is 6/78370.