GCF of 8284/614, 7259/7102
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8284/614, 7259/7102 i.e 1/2180314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8284/614, 7259/7102.
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 8284/614,7259/7102?
Given fractions are 8284/614,7259/7102
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 8284/614,7259/7102, numerators are 8284,7259
Denominators are 614,7102
The GCF of 8284,7259 is 1 .
LCM of 614,7102 is 2180314.
The greatest common factor of 8284/614,7259/7102 = [GCF of 8284,7259]/[LCM of 614,7102]= 1/2180314
Therefore, the GCF of 8284/614,7259/7102 is 1/2180314.
To find the highest common factor of 8284,7259, we have to find the factors of both numbers and list the highest common factor.
The factors of 8284 are 1, 2, 4, 19, 38, 76, 109, 218, 436, 2071, 4142, 8284
The factors of 7259 are 1, 7, 17, 61, 119, 427, 1037, 7259
The HCF of 8284,7259 is 1.
Lets's calculate GCF of 8284,7259
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8284,7259 By Matching Biggest Common Factor Method
Now, list down the factors of 8284
:1,2,4,19,38,76,109,218,436,2071,4142,8284
Now, list down the factors of 7259
:1,7,17,61,119,427,1037,7259
Greatest Common Factor
We found the factors 8284,7259 . The biggest common factor number is the GCF number.
So the greatest common factor 8284,7259 is 1.
Lets's calculate LCM of 614,7102
| 2 | 614, 7102 |
| 307, 3551 |
∴ So the LCM of the given numbers is 2 x 307 x 3551 = 2180314
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2180314
Therefore, the GCF of Fractions 8284/614,7259/7102 is 1/2180314
Least Common Multiple of 614,7102 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 614,7102 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(614,7102) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(614,7102) x common factors =2 x 1 = 2
LCM(614,7102) = ( 614 × 7102 ) / 2
LCM(614,7102) = 4360628 / 2
LCM(614,7102) = 2180314
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FAQs on GCF of Fractions of 8284/614, 7259/7102
1. What is the HCF of 8284,7259?
The HCF of 8284,7259 is 1
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 8284/614, 7259/7102?
Answer: GCF of Numerators as per given numbers 8284/614, 7259/7102 is
GCF of Numerators i.e. for 8284,7259 is 1
LCM of denominators i.e. for 614,7102 is 2180314.
Thus, GCF of Fractions is 1/2180314.Finally, GCF of Fractions for 8284/614, 7259/7102 is 1/2180314.