GCF of 6978/398, 1678/3500
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6978/398, 1678/3500 i.e 2/696500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6978/398, 1678/3500.
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 6978/398,1678/3500?
Given fractions are 6978/398,1678/3500
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 6978/398,1678/3500, numerators are 6978,1678
Denominators are 398,3500
The GCF of 6978,1678 is 2 .
LCM of 398,3500 is 696500.
The greatest common factor of 6978/398,1678/3500 = [GCF of 6978,1678]/[LCM of 398,3500]= 2/696500
Therefore, the GCF of 6978/398,1678/3500 is 2/696500.
To find the highest common factor of 6978,1678, we have to find the factors of both numbers and list the highest common factor.
The factors of 6978 are 1, 2, 3, 6, 1163, 2326, 3489, 6978
The factors of 1678 are 1, 2, 839, 1678
The HCF of 6978,1678 is 2.
Lets's calculate GCF of 6978,1678
| 2 | 6978, 1678 |
| 3489, 839 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 6978,1678 By Matching Biggest Common Factor Method
Now, list down the factors of 6978
:1,2,3,6,1163,2326,3489,6978
Now, list down the factors of 1678
:1,2,839,1678
Greatest Common Factor
We found the factors 6978,1678 . The biggest common factor number is the GCF number.
So the greatest common factor 6978,1678 is 2.
Lets's calculate LCM of 398,3500
| 2 | 398, 3500 |
| 199, 1750 |
∴ So the LCM of the given numbers is 2 x 199 x 1750 = 696500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/696500
Therefore, the GCF of Fractions 6978/398,1678/3500 is 2/696500
Least Common Multiple of 398,3500 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 398,3500 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(398,3500) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(398,3500) x common factors =2 x 1 = 2
LCM(398,3500) = ( 398 × 3500 ) / 2
LCM(398,3500) = 1393000 / 2
LCM(398,3500) = 696500
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FAQs on GCF of Fractions of 6978/398, 1678/3500
1. What is the HCF of 6978,1678?
The HCF of 6978,1678 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 6978/398, 1678/3500?
Answer: GCF of Numerators as per given numbers 6978/398, 1678/3500 is
GCF of Numerators i.e. for 6978,1678 is 2
LCM of denominators i.e. for 398,3500 is 696500.
Thus, GCF of Fractions is 2/696500.Finally, GCF of Fractions for 6978/398, 1678/3500 is 2/696500.