GCF of 3706/978, 4199/5223
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3706/978, 4199/5223 i.e 17/1702698 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3706/978, 4199/5223.
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 3706/978,4199/5223?
Given fractions are 3706/978,4199/5223
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 3706/978,4199/5223, numerators are 3706,4199
Denominators are 978,5223
The GCF of 3706,4199 is 17 .
LCM of 978,5223 is 1702698.
The greatest common factor of 3706/978,4199/5223 = [GCF of 3706,4199]/[LCM of 978,5223]= 17/1702698
Therefore, the GCF of 3706/978,4199/5223 is 17/1702698.
To find the highest common factor of 3706,4199, we have to find the factors of both numbers and list the highest common factor.
The factors of 3706 are 1, 2, 17, 34, 109, 218, 1853, 3706
The factors of 4199 are 1, 13, 17, 19, 221, 247, 323, 4199
The HCF of 3706,4199 is 17.
Lets's calculate GCF of 3706,4199
| 17 | 3706, 4199 |
| 218, 247 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 3706,4199 By Matching Biggest Common Factor Method
Now, list down the factors of 3706
:1,2,17,34,109,218,1853,3706
Now, list down the factors of 4199
:1,13,17,19,221,247,323,4199
Greatest Common Factor
We found the factors 3706,4199 . The biggest common factor number is the GCF number.
So the greatest common factor 3706,4199 is 17.
Lets's calculate LCM of 978,5223
| 3 | 978, 5223 |
| 326, 1741 |
∴ So the LCM of the given numbers is 3 x 326 x 1741 = 1702698
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/1702698
Therefore, the GCF of Fractions 3706/978,4199/5223 is 17/1702698
Least Common Multiple of 978,5223 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 978,5223 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(978,5223) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(978,5223) x common factors =3 x 1 = 3
LCM(978,5223) = ( 978 × 5223 ) / 3
LCM(978,5223) = 5108094 / 3
LCM(978,5223) = 1702698
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FAQs on GCF of Fractions of 3706/978, 4199/5223
1. What is the HCF of 3706,4199?
The HCF of 3706,4199 is 17
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 3706/978, 4199/5223?
Answer: GCF of Numerators as per given numbers 3706/978, 4199/5223 is
GCF of Numerators i.e. for 3706,4199 is 17
LCM of denominators i.e. for 978,5223 is 1702698.
Thus, GCF of Fractions is 17/1702698.Finally, GCF of Fractions for 3706/978, 4199/5223 is 17/1702698.