GCF of 972/540, 405/274
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 972/540, 405/274 i.e 81/73980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 972/540, 405/274.
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 972/540,405/274?
Given fractions are 972/540,405/274
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 972/540,405/274, numerators are 972,405
Denominators are 540,274
The GCF of 972,405 is 81 .
LCM of 540,274 is 73980.
The greatest common factor of 972/540,405/274 = [GCF of 972,405]/[LCM of 540,274]= 81/73980
Therefore, the GCF of 972/540,405/274 is 81/73980.
To find the highest common factor of 972,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 972,405 is 81.
Lets's calculate GCF of 972,405
| 3 | 972, 405 |
| 3 | 324, 135 |
| 3 | 108, 45 |
| 3 | 36, 15 |
| 12, 5 |
∴ So the GCF of the given numbers is 3 x 3 x 3 x 3 = 81
Greatest Common Factor of 972,405 By Matching Biggest Common Factor Method
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 972,405 . The biggest common factor number is the GCF number.
So the greatest common factor 972,405 is 81.
Lets's calculate LCM of 540,274
| 2 | 540, 274 |
| 270, 137 |
∴ So the LCM of the given numbers is 2 x 270 x 137 = 73980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 81/73980
Therefore, the GCF of Fractions 972/540,405/274 is 81/73980
Least Common Multiple of 540,274 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 540,274 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(540,274) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(540,274) x common factors =2 x 1 = 2
LCM(540,274) = ( 540 × 274 ) / 2
LCM(540,274) = 147960 / 2
LCM(540,274) = 73980
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FAQs on GCF of Fractions of 972/540, 405/274
1. What is the HCF of 972,405?
The HCF of 972,405 is 81
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 972/540, 405/274?
Answer: GCF of Numerators as per given numbers 972/540, 405/274 is
GCF of Numerators i.e. for 972,405 is 81
LCM of denominators i.e. for 540,274 is 73980.
Thus, GCF of Fractions is 81/73980.Finally, GCF of Fractions for 972/540, 405/274 is 81/73980.