GCF of 3126/206, 3614/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3126/206, 3614/978 i.e 2/100734 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3126/206, 3614/978.
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 3126/206,3614/978?
Given fractions are 3126/206,3614/978
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 3126/206,3614/978, numerators are 3126,3614
Denominators are 206,978
The GCF of 3126,3614 is 2 .
LCM of 206,978 is 100734.
The greatest common factor of 3126/206,3614/978 = [GCF of 3126,3614]/[LCM of 206,978]= 2/100734
Therefore, the GCF of 3126/206,3614/978 is 2/100734.
To find the highest common factor of 3126,3614, we have to find the factors of both numbers and list the highest common factor.
The factors of 3126 are 1, 2, 3, 6, 521, 1042, 1563, 3126
The factors of 3614 are 1, 2, 13, 26, 139, 278, 1807, 3614
The HCF of 3126,3614 is 2.
Lets's calculate GCF of 3126,3614
| 2 | 3126, 3614 |
| 1563, 1807 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 3126,3614 By Matching Biggest Common Factor Method
Now, list down the factors of 3126
:1,2,3,6,521,1042,1563,3126
Now, list down the factors of 3614
:1,2,13,26,139,278,1807,3614
Greatest Common Factor
We found the factors 3126,3614 . The biggest common factor number is the GCF number.
So the greatest common factor 3126,3614 is 2.
Lets's calculate LCM of 206,978
| 2 | 206, 978 |
| 103, 489 |
∴ So the LCM of the given numbers is 2 x 103 x 489 = 100734
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/100734
Therefore, the GCF of Fractions 3126/206,3614/978 is 2/100734
Least Common Multiple of 206,978 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 206,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(206,978) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(206,978) x common factors =2 x 1 = 2
LCM(206,978) = ( 206 × 978 ) / 2
LCM(206,978) = 201468 / 2
LCM(206,978) = 100734
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FAQs on GCF of Fractions of 3126/206, 3614/978
1. What is the HCF of 3126,3614?
The HCF of 3126,3614 is 2
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 3126/206, 3614/978?
Answer: GCF of Numerators as per given numbers 3126/206, 3614/978 is
GCF of Numerators i.e. for 3126,3614 is 2
LCM of denominators i.e. for 206,978 is 100734.
Thus, GCF of Fractions is 2/100734.Finally, GCF of Fractions for 3126/206, 3614/978 is 2/100734.