GCF of 189/540, 486/975
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 189/540, 486/975 i.e 27/35100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 189/540, 486/975.
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 189/540,486/975?
Given fractions are 189/540,486/975
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 189/540,486/975, numerators are 189,486
Denominators are 540,975
The GCF of 189,486 is 27 .
LCM of 540,975 is 35100.
The greatest common factor of 189/540,486/975 = [GCF of 189,486]/[LCM of 540,975]= 27/35100
Therefore, the GCF of 189/540,486/975 is 27/35100.
To find the highest common factor of 189,486, we have to find the factors of both numbers and list the highest common factor.
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The factors of 486 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486
The HCF of 189,486 is 27.
Lets's calculate GCF of 189,486
| 3 | 189, 486 |
| 3 | 63, 162 |
| 3 | 21, 54 |
| 7, 18 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 189,486 By Matching Biggest Common Factor Method
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Now, list down the factors of 486
:1,2,3,6,9,18,27,54,81,162,243,486
Greatest Common Factor
We found the factors 189,486 . The biggest common factor number is the GCF number.
So the greatest common factor 189,486 is 27.
Lets's calculate LCM of 540,975
| 3 | 540, 975 |
| 5 | 180, 325 |
| 36, 65 |
∴ So the LCM of the given numbers is 3 x 5 x 36 x 65 = 35100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/35100
Therefore, the GCF of Fractions 189/540,486/975 is 27/35100
Least Common Multiple of 540,975 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 540,975 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(540,975) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(540,975) x common factors =15 x 1 = 15
LCM(540,975) = ( 540 × 975 ) / 15
LCM(540,975) = 526500 / 15
LCM(540,975) = 35100
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FAQs on GCF of Fractions of 189/540, 486/975
1. What is the HCF of 189,486?
The HCF of 189,486 is 27
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 189/540, 486/975?
Answer: GCF of Numerators as per given numbers 189/540, 486/975 is
GCF of Numerators i.e. for 189,486 is 27
LCM of denominators i.e. for 540,975 is 35100.
Thus, GCF of Fractions is 27/35100.Finally, GCF of Fractions for 189/540, 486/975 is 27/35100.