GCF of 3174/318, 1677/7317
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3174/318, 1677/7317 i.e 3/775602 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3174/318, 1677/7317.
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 3174/318,1677/7317?
Given fractions are 3174/318,1677/7317
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 3174/318,1677/7317, numerators are 3174,1677
Denominators are 318,7317
The GCF of 3174,1677 is 3 .
LCM of 318,7317 is 775602.
The greatest common factor of 3174/318,1677/7317 = [GCF of 3174,1677]/[LCM of 318,7317]= 3/775602
Therefore, the GCF of 3174/318,1677/7317 is 3/775602.
To find the highest common factor of 3174,1677, we have to find the factors of both numbers and list the highest common factor.
The factors of 3174 are 1, 2, 3, 6, 23, 46, 69, 138, 529, 1058, 1587, 3174
The factors of 1677 are 1, 3, 13, 39, 43, 129, 559, 1677
The HCF of 3174,1677 is 3.
Lets's calculate GCF of 3174,1677
| 3 | 3174, 1677 |
| 1058, 559 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3174,1677 By Matching Biggest Common Factor Method
Now, list down the factors of 3174
:1,2,3,6,23,46,69,138,529,1058,1587,3174
Now, list down the factors of 1677
:1,3,13,39,43,129,559,1677
Greatest Common Factor
We found the factors 3174,1677 . The biggest common factor number is the GCF number.
So the greatest common factor 3174,1677 is 3.
Lets's calculate LCM of 318,7317
| 3 | 318, 7317 |
| 106, 2439 |
∴ So the LCM of the given numbers is 3 x 106 x 2439 = 775602
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/775602
Therefore, the GCF of Fractions 3174/318,1677/7317 is 3/775602
Least Common Multiple of 318,7317 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 318,7317 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(318,7317) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(318,7317) x common factors =3 x 1 = 3
LCM(318,7317) = ( 318 × 7317 ) / 3
LCM(318,7317) = 2326806 / 3
LCM(318,7317) = 775602
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FAQs on GCF of Fractions of 3174/318, 1677/7317
1. What is the HCF of 3174,1677?
The HCF of 3174,1677 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 3174/318, 1677/7317?
Answer: GCF of Numerators as per given numbers 3174/318, 1677/7317 is
GCF of Numerators i.e. for 3174,1677 is 3
LCM of denominators i.e. for 318,7317 is 775602.
Thus, GCF of Fractions is 3/775602.Finally, GCF of Fractions for 3174/318, 1677/7317 is 3/775602.