GCF of 3970/270, 1310/582
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3970/270, 1310/582 i.e 10/26190 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3970/270, 1310/582.
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 3970/270,1310/582?
Given fractions are 3970/270,1310/582
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 3970/270,1310/582, numerators are 3970,1310
Denominators are 270,582
The GCF of 3970,1310 is 10 .
LCM of 270,582 is 26190.
The greatest common factor of 3970/270,1310/582 = [GCF of 3970,1310]/[LCM of 270,582]= 10/26190
Therefore, the GCF of 3970/270,1310/582 is 10/26190.
To find the highest common factor of 3970,1310, we have to find the factors of both numbers and list the highest common factor.
The factors of 3970 are 1, 2, 5, 10, 397, 794, 1985, 3970
The factors of 1310 are 1, 2, 5, 10, 131, 262, 655, 1310
The HCF of 3970,1310 is 10.
Lets's calculate GCF of 3970,1310
| 2 | 3970, 1310 |
| 5 | 1985, 655 |
| 397, 131 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 3970,1310 By Matching Biggest Common Factor Method
Now, list down the factors of 3970
:1,2,5,10,397,794,1985,3970
Now, list down the factors of 1310
:1,2,5,10,131,262,655,1310
Greatest Common Factor
We found the factors 3970,1310 . The biggest common factor number is the GCF number.
So the greatest common factor 3970,1310 is 10.
Lets's calculate LCM of 270,582
| 2 | 270, 582 |
| 3 | 135, 291 |
| 45, 97 |
∴ So the LCM of the given numbers is 2 x 3 x 45 x 97 = 26190
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/26190
Therefore, the GCF of Fractions 3970/270,1310/582 is 10/26190
Least Common Multiple of 270,582 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 270,582 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,582) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(270,582) x common factors =6 x 1 = 6
LCM(270,582) = ( 270 × 582 ) / 6
LCM(270,582) = 157140 / 6
LCM(270,582) = 26190
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FAQs on GCF of Fractions of 3970/270, 1310/582
1. What is the HCF of 3970,1310?
The HCF of 3970,1310 is 10
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 3970/270, 1310/582?
Answer: GCF of Numerators as per given numbers 3970/270, 1310/582 is
GCF of Numerators i.e. for 3970,1310 is 10
LCM of denominators i.e. for 270,582 is 26190.
Thus, GCF of Fractions is 10/26190.Finally, GCF of Fractions for 3970/270, 1310/582 is 10/26190.