GCF of 540/532, 7830/159
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 540/532, 7830/159 i.e 270/84588 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/532, 7830/159.
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 540/532,7830/159?
Given fractions are 540/532,7830/159
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 540/532,7830/159, numerators are 540,7830
Denominators are 532,159
The GCF of 540,7830 is 270 .
LCM of 532,159 is 84588.
The greatest common factor of 540/532,7830/159 = [GCF of 540,7830]/[LCM of 532,159]= 270/84588
Therefore, the GCF of 540/532,7830/159 is 270/84588.
To find the highest common factor of 540,7830, we have to find the factors of both numbers and list the highest common factor.
The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The factors of 7830 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 29, 30, 45, 54, 58, 87, 90, 135, 145, 174, 261, 270, 290, 435, 522, 783, 870, 1305, 1566, 2610, 3915, 7830
The HCF of 540,7830 is 270.
Lets's calculate GCF of 540,7830
| 2 | 540, 7830 |
| 3 | 270, 3915 |
| 3 | 90, 1305 |
| 3 | 30, 435 |
| 5 | 10, 145 |
| 2, 29 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 x 5 = 270
Greatest Common Factor of 540,7830 By Matching Biggest Common Factor Method
Now, list down the factors of 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Now, list down the factors of 7830
:1,2,3,5,6,9,10,15,18,27,29,30,45,54,58,87,90,135,145,174,261,270,290,435,522,783,870,1305,1566,2610,3915,7830
Greatest Common Factor
We found the factors 540,7830 . The biggest common factor number is the GCF number.
So the greatest common factor 540,7830 is 270.
Lets's calculate LCM of 532,159
Given numbers has no common factors except 1. So, there LCM is their product i.e 84588
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 270/84588
Therefore, the GCF of Fractions 540/532,7830/159 is 270/84588
Least Common Multiple of 532,159 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 532,159 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(532,159) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(532,159) x common factors =1 x 1 = 1
LCM(532,159) = ( 532 × 159 ) / 1
LCM(532,159) = 84588 / 1
LCM(532,159) = 84588
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FAQs on GCF of Fractions of 540/532, 7830/159
1. What is the HCF of 540,7830?
The HCF of 540,7830 is 270
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 540/532, 7830/159?
Answer: GCF of Numerators as per given numbers 540/532, 7830/159 is
GCF of Numerators i.e. for 540,7830 is 270
LCM of denominators i.e. for 532,159 is 84588.
Thus, GCF of Fractions is 270/84588.Finally, GCF of Fractions for 540/532, 7830/159 is 270/84588.