GCF of 7412/839, 2109/2123
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7412/839, 2109/2123 i.e 1/1781197 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7412/839, 2109/2123.
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 7412/839,2109/2123?
Given fractions are 7412/839,2109/2123
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 7412/839,2109/2123, numerators are 7412,2109
Denominators are 839,2123
The GCF of 7412,2109 is 1 .
LCM of 839,2123 is 1781197.
The greatest common factor of 7412/839,2109/2123 = [GCF of 7412,2109]/[LCM of 839,2123]= 1/1781197
Therefore, the GCF of 7412/839,2109/2123 is 1/1781197.
To find the highest common factor of 7412,2109, we have to find the factors of both numbers and list the highest common factor.
The factors of 7412 are 1, 2, 4, 17, 34, 68, 109, 218, 436, 1853, 3706, 7412
The factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109
The HCF of 7412,2109 is 1.
Lets's calculate GCF of 7412,2109
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7412,2109 By Matching Biggest Common Factor Method
Now, list down the factors of 7412
:1,2,4,17,34,68,109,218,436,1853,3706,7412
Now, list down the factors of 2109
:1,3,19,37,57,111,703,2109
Greatest Common Factor
We found the factors 7412,2109 . The biggest common factor number is the GCF number.
So the greatest common factor 7412,2109 is 1.
Lets's calculate LCM of 839,2123
Given numbers has no common factors except 1. So, there LCM is their product i.e 1781197
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1781197
Therefore, the GCF of Fractions 7412/839,2109/2123 is 1/1781197
Least Common Multiple of 839,2123 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 839,2123 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(839,2123) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(839,2123) x common factors =1 x 1 = 1
LCM(839,2123) = ( 839 × 2123 ) / 1
LCM(839,2123) = 1781197 / 1
LCM(839,2123) = 1781197
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FAQs on GCF of Fractions of 7412/839, 2109/2123
1. What is the HCF of 7412,2109?
The HCF of 7412,2109 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 7412/839, 2109/2123?
Answer: GCF of Numerators as per given numbers 7412/839, 2109/2123 is
GCF of Numerators i.e. for 7412,2109 is 1
LCM of denominators i.e. for 839,2123 is 1781197.
Thus, GCF of Fractions is 1/1781197.Finally, GCF of Fractions for 7412/839, 2109/2123 is 1/1781197.