GCF of 165/245, 180/392, 210/486
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 165/245, 180/392, 210/486 i.e 15/476280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 165/245, 180/392, 210/486.
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 165/245,180/392,210/486?
Given fractions are 165/245,180/392,210/486
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 165/245,180/392,210/486, numerators are 165,180,210
Denominators are 245,392,486
The GCF of 165,180,210 is 15 .
LCM of 245,392,486 is 476280.
The greatest common factor of 165/245,180/392,210/486 = [GCF of 165,180,210]/[LCM of 245,392,486]= 15/476280
Therefore, the GCF of 165/245,180/392,210/486 is 15/476280.
To find the highest common factor of 165,180,210, we have to find the factors of both numbers and list the highest common factor.
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 165,180,210 is 15.
Lets's calculate GCF of 165,180,210
| 3 | 165, 180, 210 |
| 5 | 55, 60, 70 |
| 11, 12, 14 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 165,180,210 By Matching Biggest Common Factor Method
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Now, list down the factors of 180
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 165,180,210 . The biggest common factor number is the GCF number.
So the greatest common factor 165,180,210 is 15.
Lets's calculate LCM of 245,392,486
| 2 | 245, 392, 486 |
| 7 | 245, 196, 243 |
| 7 | 35, 28, 243 |
| 5, 4, 243 |
∴ So the LCM of the given numbers is 2 x 7 x 7 x 5 x 4 x 243 = 476280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/476280
Therefore, the GCF of Fractions 165/245,180/392,210/486 is 15/476280
Least Common Multiple of 245,392,486 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 245,392,486 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(245,392,486) = 1
common factors(in case of two or more numbers have common factors) = 98
GCF(245,392,486) x common factors =1 x 98 = 98
LCM(245,392,486) = ( 245 × 392 × 486 ) / 98
LCM(245,392,486) = 46675440 / 98
LCM(245,392,486) = 476280
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 165/245, 180/392, 210/486
1. What is the HCF of 165,180,210?
The HCF of 165,180,210 is 15
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 165/245, 180/392, 210/486?
Answer: GCF of Numerators as per given numbers 165/245, 180/392, 210/486 is
GCF of Numerators i.e. for 165,180,210 is 15
LCM of denominators i.e. for 245,392,486 is 476280.
Thus, GCF of Fractions is 15/476280.Finally, GCF of Fractions for 165/245, 180/392, 210/486 is 15/476280.