GCF of 7970/32, 5176/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7970/32, 5176/978 i.e 2/15648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7970/32, 5176/978.
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 7970/32,5176/978?
Given fractions are 7970/32,5176/978
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 7970/32,5176/978, numerators are 7970,5176
Denominators are 32,978
The GCF of 7970,5176 is 2 .
LCM of 32,978 is 15648.
The greatest common factor of 7970/32,5176/978 = [GCF of 7970,5176]/[LCM of 32,978]= 2/15648
Therefore, the GCF of 7970/32,5176/978 is 2/15648.
To find the highest common factor of 7970,5176, we have to find the factors of both numbers and list the highest common factor.
The factors of 7970 are 1, 2, 5, 10, 797, 1594, 3985, 7970
The factors of 5176 are 1, 2, 4, 8, 647, 1294, 2588, 5176
The HCF of 7970,5176 is 2.
Lets's calculate GCF of 7970,5176
| 2 | 7970, 5176 |
| 3985, 2588 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7970,5176 By Matching Biggest Common Factor Method
Now, list down the factors of 7970
:1,2,5,10,797,1594,3985,7970
Now, list down the factors of 5176
:1,2,4,8,647,1294,2588,5176
Greatest Common Factor
We found the factors 7970,5176 . The biggest common factor number is the GCF number.
So the greatest common factor 7970,5176 is 2.
Lets's calculate LCM of 32,978
| 2 | 32, 978 |
| 16, 489 |
∴ So the LCM of the given numbers is 2 x 16 x 489 = 15648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/15648
Therefore, the GCF of Fractions 7970/32,5176/978 is 2/15648
Least Common Multiple of 32,978 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 32,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,978) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(32,978) x common factors =2 x 1 = 2
LCM(32,978) = ( 32 × 978 ) / 2
LCM(32,978) = 31296 / 2
LCM(32,978) = 15648
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FAQs on GCF of Fractions of 7970/32, 5176/978
1. What is the HCF of 7970,5176?
The HCF of 7970,5176 is 2
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 7970/32, 5176/978?
Answer: GCF of Numerators as per given numbers 7970/32, 5176/978 is
GCF of Numerators i.e. for 7970,5176 is 2
LCM of denominators i.e. for 32,978 is 15648.
Thus, GCF of Fractions is 2/15648.Finally, GCF of Fractions for 7970/32, 5176/978 is 2/15648.