GCF of 5940/270, 7134/5169
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5940/270, 7134/5169 i.e 6/465210 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5940/270, 7134/5169.
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 5940/270,7134/5169?
Given fractions are 5940/270,7134/5169
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 5940/270,7134/5169, numerators are 5940,7134
Denominators are 270,5169
The GCF of 5940,7134 is 6 .
LCM of 270,5169 is 465210.
The greatest common factor of 5940/270,7134/5169 = [GCF of 5940,7134]/[LCM of 270,5169]= 6/465210
Therefore, the GCF of 5940/270,7134/5169 is 6/465210.
To find the highest common factor of 5940,7134, we have to find the factors of both numbers and list the highest common factor.
The factors of 5940 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30, 33, 36, 44, 45, 54, 55, 60, 66, 90, 99, 108, 110, 132, 135, 165, 180, 198, 220, 270, 297, 330, 396, 495, 540, 594, 660, 990, 1188, 1485, 1980, 2970, 5940
The factors of 7134 are 1, 2, 3, 6, 29, 41, 58, 82, 87, 123, 174, 246, 1189, 2378, 3567, 7134
The HCF of 5940,7134 is 6.
Lets's calculate GCF of 5940,7134
| 2 | 5940, 7134 |
| 3 | 2970, 3567 |
| 990, 1189 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 5940,7134 By Matching Biggest Common Factor Method
Now, list down the factors of 5940
:1,2,3,4,5,6,9,10,11,12,15,18,20,22,27,30,33,36,44,45,54,55,60,66,90,99,108,110,132,135,165,180,198,220,270,297,330,396,495,540,594,660,990,1188,1485,1980,2970,5940
Now, list down the factors of 7134
:1,2,3,6,29,41,58,82,87,123,174,246,1189,2378,3567,7134
Greatest Common Factor
We found the factors 5940,7134 . The biggest common factor number is the GCF number.
So the greatest common factor 5940,7134 is 6.
Lets's calculate LCM of 270,5169
| 3 | 270, 5169 |
| 90, 1723 |
∴ So the LCM of the given numbers is 3 x 90 x 1723 = 465210
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/465210
Therefore, the GCF of Fractions 5940/270,7134/5169 is 6/465210
Least Common Multiple of 270,5169 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 270,5169 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,5169) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(270,5169) x common factors =3 x 1 = 3
LCM(270,5169) = ( 270 × 5169 ) / 3
LCM(270,5169) = 1395630 / 3
LCM(270,5169) = 465210
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 5940/270, 7134/5169
1. What is the HCF of 5940,7134?
The HCF of 5940,7134 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 5940/270, 7134/5169?
Answer: GCF of Numerators as per given numbers 5940/270, 7134/5169 is
GCF of Numerators i.e. for 5940,7134 is 6
LCM of denominators i.e. for 270,5169 is 465210.
Thus, GCF of Fractions is 6/465210.Finally, GCF of Fractions for 5940/270, 7134/5169 is 6/465210.