GCF of 7314/318, 6187/6318
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7314/318, 6187/6318 i.e 23/334854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7314/318, 6187/6318.
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 7314/318,6187/6318?
Given fractions are 7314/318,6187/6318
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 7314/318,6187/6318, numerators are 7314,6187
Denominators are 318,6318
The GCF of 7314,6187 is 23 .
LCM of 318,6318 is 334854.
The greatest common factor of 7314/318,6187/6318 = [GCF of 7314,6187]/[LCM of 318,6318]= 23/334854
Therefore, the GCF of 7314/318,6187/6318 is 23/334854.
To find the highest common factor of 7314,6187, we have to find the factors of both numbers and list the highest common factor.
The factors of 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314
The factors of 6187 are 1, 23, 269, 6187
The HCF of 7314,6187 is 23.
Lets's calculate GCF of 7314,6187
| 23 | 7314, 6187 |
| 318, 269 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 7314,6187 By Matching Biggest Common Factor Method
Now, list down the factors of 7314
:1,2,3,6,23,46,53,69,106,138,159,318,1219,2438,3657,7314
Now, list down the factors of 6187
:1,23,269,6187
Greatest Common Factor
We found the factors 7314,6187 . The biggest common factor number is the GCF number.
So the greatest common factor 7314,6187 is 23.
Lets's calculate LCM of 318,6318
| 2 | 318, 6318 |
| 3 | 159, 3159 |
| 53, 1053 |
∴ So the LCM of the given numbers is 2 x 3 x 53 x 1053 = 334854
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/334854
Therefore, the GCF of Fractions 7314/318,6187/6318 is 23/334854
Least Common Multiple of 318,6318 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 318,6318 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(318,6318) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(318,6318) x common factors =6 x 1 = 6
LCM(318,6318) = ( 318 × 6318 ) / 6
LCM(318,6318) = 2009124 / 6
LCM(318,6318) = 334854
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FAQs on GCF of Fractions of 7314/318, 6187/6318
1. What is the HCF of 7314,6187?
The HCF of 7314,6187 is 23
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 7314/318, 6187/6318?
Answer: GCF of Numerators as per given numbers 7314/318, 6187/6318 is
GCF of Numerators i.e. for 7314,6187 is 23
LCM of denominators i.e. for 318,6318 is 334854.
Thus, GCF of Fractions is 23/334854.Finally, GCF of Fractions for 7314/318, 6187/6318 is 23/334854.