GCF of 2109/142, 3462/1969
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2109/142, 3462/1969 i.e 3/279598 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2109/142, 3462/1969.
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 2109/142,3462/1969?
Given fractions are 2109/142,3462/1969
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 2109/142,3462/1969, numerators are 2109,3462
Denominators are 142,1969
The GCF of 2109,3462 is 3 .
LCM of 142,1969 is 279598.
The greatest common factor of 2109/142,3462/1969 = [GCF of 2109,3462]/[LCM of 142,1969]= 3/279598
Therefore, the GCF of 2109/142,3462/1969 is 3/279598.
To find the highest common factor of 2109,3462, we have to find the factors of both numbers and list the highest common factor.
The factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109
The factors of 3462 are 1, 2, 3, 6, 577, 1154, 1731, 3462
The HCF of 2109,3462 is 3.
Lets's calculate GCF of 2109,3462
| 3 | 2109, 3462 |
| 703, 1154 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2109,3462 By Matching Biggest Common Factor Method
Now, list down the factors of 2109
:1,3,19,37,57,111,703,2109
Now, list down the factors of 3462
:1,2,3,6,577,1154,1731,3462
Greatest Common Factor
We found the factors 2109,3462 . The biggest common factor number is the GCF number.
So the greatest common factor 2109,3462 is 3.
Lets's calculate LCM of 142,1969
Given numbers has no common factors except 1. So, there LCM is their product i.e 279598
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/279598
Therefore, the GCF of Fractions 2109/142,3462/1969 is 3/279598
Least Common Multiple of 142,1969 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 142,1969 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(142,1969) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(142,1969) x common factors =1 x 1 = 1
LCM(142,1969) = ( 142 × 1969 ) / 1
LCM(142,1969) = 279598 / 1
LCM(142,1969) = 279598
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FAQs on GCF of Fractions of 2109/142, 3462/1969
1. What is the HCF of 2109,3462?
The HCF of 2109,3462 is 3
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 2109/142, 3462/1969?
Answer: GCF of Numerators as per given numbers 2109/142, 3462/1969 is
GCF of Numerators i.e. for 2109,3462 is 3
LCM of denominators i.e. for 142,1969 is 279598.
Thus, GCF of Fractions is 3/279598.Finally, GCF of Fractions for 2109/142, 3462/1969 is 3/279598.