GCF of 351/21, 658/1980
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 351/21, 658/1980 i.e 1/13860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 351/21, 658/1980.
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 351/21,658/1980?
Given fractions are 351/21,658/1980
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 351/21,658/1980, numerators are 351,658
Denominators are 21,1980
The GCF of 351,658 is 1 .
LCM of 21,1980 is 13860.
The greatest common factor of 351/21,658/1980 = [GCF of 351,658]/[LCM of 21,1980]= 1/13860
Therefore, the GCF of 351/21,658/1980 is 1/13860.
To find the highest common factor of 351,658, we have to find the factors of both numbers and list the highest common factor.
The factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351
The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658
The HCF of 351,658 is 1.
Lets's calculate GCF of 351,658
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 351,658 By Matching Biggest Common Factor Method
Now, list down the factors of 351
:1,3,9,13,27,39,117,351
Now, list down the factors of 658
:1,2,7,14,47,94,329,658
Greatest Common Factor
We found the factors 351,658 . The biggest common factor number is the GCF number.
So the greatest common factor 351,658 is 1.
Lets's calculate LCM of 21,1980
| 3 | 21, 1980 |
| 7, 660 |
∴ So the LCM of the given numbers is 3 x 7 x 660 = 13860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13860
Therefore, the GCF of Fractions 351/21,658/1980 is 1/13860
Least Common Multiple of 21,1980 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 21,1980 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,1980) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(21,1980) x common factors =3 x 1 = 3
LCM(21,1980) = ( 21 × 1980 ) / 3
LCM(21,1980) = 41580 / 3
LCM(21,1980) = 13860
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FAQs on GCF of Fractions of 351/21, 658/1980
1. What is the HCF of 351,658?
The HCF of 351,658 is 1
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 351/21, 658/1980?
Answer: GCF of Numerators as per given numbers 351/21, 658/1980 is
GCF of Numerators i.e. for 351,658 is 1
LCM of denominators i.e. for 21,1980 is 13860.
Thus, GCF of Fractions is 1/13860.Finally, GCF of Fractions for 351/21, 658/1980 is 1/13860.