GCF of 3109/218, 9990/7642
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3109/218, 9990/7642 i.e 1/832978 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3109/218, 9990/7642.
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 3109/218,9990/7642?
Given fractions are 3109/218,9990/7642
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 3109/218,9990/7642, numerators are 3109,9990
Denominators are 218,7642
The GCF of 3109,9990 is 1 .
LCM of 218,7642 is 832978.
The greatest common factor of 3109/218,9990/7642 = [GCF of 3109,9990]/[LCM of 218,7642]= 1/832978
Therefore, the GCF of 3109/218,9990/7642 is 1/832978.
To find the highest common factor of 3109,9990, we have to find the factors of both numbers and list the highest common factor.
The factors of 3109 are 1, 3109
The factors of 9990 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 37, 45, 54, 74, 90, 111, 135, 185, 222, 270, 333, 370, 555, 666, 999, 1110, 1665, 1998, 3330, 4995, 9990
The HCF of 3109,9990 is 1.
Lets's calculate GCF of 3109,9990
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3109,9990 By Matching Biggest Common Factor Method
Now, list down the factors of 3109
:1,3109
Now, list down the factors of 9990
:1,2,3,5,6,9,10,15,18,27,30,37,45,54,74,90,111,135,185,222,270,333,370,555,666,999,1110,1665,1998,3330,4995,9990
Greatest Common Factor
We found the factors 3109,9990 . The biggest common factor number is the GCF number.
So the greatest common factor 3109,9990 is 1.
Lets's calculate LCM of 218,7642
| 2 | 218, 7642 |
| 109, 3821 |
∴ So the LCM of the given numbers is 2 x 109 x 3821 = 832978
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/832978
Therefore, the GCF of Fractions 3109/218,9990/7642 is 1/832978
Least Common Multiple of 218,7642 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 218,7642 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,7642) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(218,7642) x common factors =2 x 1 = 2
LCM(218,7642) = ( 218 × 7642 ) / 2
LCM(218,7642) = 1665956 / 2
LCM(218,7642) = 832978
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FAQs on GCF of Fractions of 3109/218, 9990/7642
1. What is the HCF of 3109,9990?
The HCF of 3109,9990 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 3109/218, 9990/7642?
Answer: GCF of Numerators as per given numbers 3109/218, 9990/7642 is
GCF of Numerators i.e. for 3109,9990 is 1
LCM of denominators i.e. for 218,7642 is 832978.
Thus, GCF of Fractions is 1/832978.Finally, GCF of Fractions for 3109/218, 9990/7642 is 1/832978.