GCF of 2978/758, 3206/8186
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2978/758, 3206/8186 i.e 2/3102494 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2978/758, 3206/8186.
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 2978/758,3206/8186?
Given fractions are 2978/758,3206/8186
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 2978/758,3206/8186, numerators are 2978,3206
Denominators are 758,8186
The GCF of 2978,3206 is 2 .
LCM of 758,8186 is 3102494.
The greatest common factor of 2978/758,3206/8186 = [GCF of 2978,3206]/[LCM of 758,8186]= 2/3102494
Therefore, the GCF of 2978/758,3206/8186 is 2/3102494.
To find the highest common factor of 2978,3206, we have to find the factors of both numbers and list the highest common factor.
The factors of 2978 are 1, 2, 1489, 2978
The factors of 3206 are 1, 2, 7, 14, 229, 458, 1603, 3206
The HCF of 2978,3206 is 2.
Lets's calculate GCF of 2978,3206
| 2 | 2978, 3206 |
| 1489, 1603 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2978,3206 By Matching Biggest Common Factor Method
Now, list down the factors of 2978
:1,2,1489,2978
Now, list down the factors of 3206
:1,2,7,14,229,458,1603,3206
Greatest Common Factor
We found the factors 2978,3206 . The biggest common factor number is the GCF number.
So the greatest common factor 2978,3206 is 2.
Lets's calculate LCM of 758,8186
| 2 | 758, 8186 |
| 379, 4093 |
∴ So the LCM of the given numbers is 2 x 379 x 4093 = 3102494
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3102494
Therefore, the GCF of Fractions 2978/758,3206/8186 is 2/3102494
Least Common Multiple of 758,8186 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 758,8186 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(758,8186) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(758,8186) x common factors =2 x 1 = 2
LCM(758,8186) = ( 758 × 8186 ) / 2
LCM(758,8186) = 6204988 / 2
LCM(758,8186) = 3102494
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FAQs on GCF of Fractions of 2978/758, 3206/8186
1. What is the HCF of 2978,3206?
The HCF of 2978,3206 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 2978/758, 3206/8186?
Answer: GCF of Numerators as per given numbers 2978/758, 3206/8186 is
GCF of Numerators i.e. for 2978,3206 is 2
LCM of denominators i.e. for 758,8186 is 3102494.
Thus, GCF of Fractions is 2/3102494.Finally, GCF of Fractions for 2978/758, 3206/8186 is 2/3102494.