GCF of 8170/315, 7314/4718
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8170/315, 7314/4718 i.e 2/212310 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8170/315, 7314/4718.
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 8170/315,7314/4718?
Given fractions are 8170/315,7314/4718
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 8170/315,7314/4718, numerators are 8170,7314
Denominators are 315,4718
The GCF of 8170,7314 is 2 .
LCM of 315,4718 is 212310.
The greatest common factor of 8170/315,7314/4718 = [GCF of 8170,7314]/[LCM of 315,4718]= 2/212310
Therefore, the GCF of 8170/315,7314/4718 is 2/212310.
To find the highest common factor of 8170,7314, we have to find the factors of both numbers and list the highest common factor.
The factors of 8170 are 1, 2, 5, 10, 19, 38, 43, 86, 95, 190, 215, 430, 817, 1634, 4085, 8170
The factors of 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314
The HCF of 8170,7314 is 2.
Lets's calculate GCF of 8170,7314
| 2 | 8170, 7314 |
| 4085, 3657 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8170,7314 By Matching Biggest Common Factor Method
Now, list down the factors of 8170
:1,2,5,10,19,38,43,86,95,190,215,430,817,1634,4085,8170
Now, list down the factors of 7314
:1,2,3,6,23,46,53,69,106,138,159,318,1219,2438,3657,7314
Greatest Common Factor
We found the factors 8170,7314 . The biggest common factor number is the GCF number.
So the greatest common factor 8170,7314 is 2.
Lets's calculate LCM of 315,4718
| 7 | 315, 4718 |
| 45, 674 |
∴ So the LCM of the given numbers is 7 x 45 x 674 = 212310
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/212310
Therefore, the GCF of Fractions 8170/315,7314/4718 is 2/212310
Least Common Multiple of 315,4718 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 315,4718 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(315,4718) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(315,4718) x common factors =7 x 1 = 7
LCM(315,4718) = ( 315 × 4718 ) / 7
LCM(315,4718) = 1486170 / 7
LCM(315,4718) = 212310
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FAQs on GCF of Fractions of 8170/315, 7314/4718
1. What is the HCF of 8170,7314?
The HCF of 8170,7314 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 8170/315, 7314/4718?
Answer: GCF of Numerators as per given numbers 8170/315, 7314/4718 is
GCF of Numerators i.e. for 8170,7314 is 2
LCM of denominators i.e. for 315,4718 is 212310.
Thus, GCF of Fractions is 2/212310.Finally, GCF of Fractions for 8170/315, 7314/4718 is 2/212310.