GCF of 3978/416, 5322/5058
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3978/416, 5322/5058 i.e 6/1052064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3978/416, 5322/5058.
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 3978/416,5322/5058?
Given fractions are 3978/416,5322/5058
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 3978/416,5322/5058, numerators are 3978,5322
Denominators are 416,5058
The GCF of 3978,5322 is 6 .
LCM of 416,5058 is 1052064.
The greatest common factor of 3978/416,5322/5058 = [GCF of 3978,5322]/[LCM of 416,5058]= 6/1052064
Therefore, the GCF of 3978/416,5322/5058 is 6/1052064.
To find the highest common factor of 3978,5322, we have to find the factors of both numbers and list the highest common factor.
The factors of 3978 are 1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153, 221, 234, 306, 442, 663, 1326, 1989, 3978
The factors of 5322 are 1, 2, 3, 6, 887, 1774, 2661, 5322
The HCF of 3978,5322 is 6.
Lets's calculate GCF of 3978,5322
| 2 | 3978, 5322 |
| 3 | 1989, 2661 |
| 663, 887 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 3978,5322 By Matching Biggest Common Factor Method
Now, list down the factors of 3978
:1,2,3,6,9,13,17,18,26,34,39,51,78,102,117,153,221,234,306,442,663,1326,1989,3978
Now, list down the factors of 5322
:1,2,3,6,887,1774,2661,5322
Greatest Common Factor
We found the factors 3978,5322 . The biggest common factor number is the GCF number.
So the greatest common factor 3978,5322 is 6.
Lets's calculate LCM of 416,5058
| 2 | 416, 5058 |
| 208, 2529 |
∴ So the LCM of the given numbers is 2 x 208 x 2529 = 1052064
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1052064
Therefore, the GCF of Fractions 3978/416,5322/5058 is 6/1052064
Least Common Multiple of 416,5058 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 416,5058 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(416,5058) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(416,5058) x common factors =2 x 1 = 2
LCM(416,5058) = ( 416 × 5058 ) / 2
LCM(416,5058) = 2104128 / 2
LCM(416,5058) = 1052064
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FAQs on GCF of Fractions of 3978/416, 5322/5058
1. What is the HCF of 3978,5322?
The HCF of 3978,5322 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 3978/416, 5322/5058?
Answer: GCF of Numerators as per given numbers 3978/416, 5322/5058 is
GCF of Numerators i.e. for 3978,5322 is 6
LCM of denominators i.e. for 416,5058 is 1052064.
Thus, GCF of Fractions is 6/1052064.Finally, GCF of Fractions for 3978/416, 5322/5058 is 6/1052064.