GCF of 7314/722, 1842/7685
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7314/722, 1842/7685 i.e 6/5548570 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7314/722, 1842/7685.
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 7314/722,1842/7685?
Given fractions are 7314/722,1842/7685
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 7314/722,1842/7685, numerators are 7314,1842
Denominators are 722,7685
The GCF of 7314,1842 is 6 .
LCM of 722,7685 is 5548570.
The greatest common factor of 7314/722,1842/7685 = [GCF of 7314,1842]/[LCM of 722,7685]= 6/5548570
Therefore, the GCF of 7314/722,1842/7685 is 6/5548570.
To find the highest common factor of 7314,1842, 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 1842 are 1, 2, 3, 6, 307, 614, 921, 1842
The HCF of 7314,1842 is 6.
Lets's calculate GCF of 7314,1842
| 2 | 7314, 1842 |
| 3 | 3657, 921 |
| 1219, 307 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 7314,1842 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 1842
:1,2,3,6,307,614,921,1842
Greatest Common Factor
We found the factors 7314,1842 . The biggest common factor number is the GCF number.
So the greatest common factor 7314,1842 is 6.
Lets's calculate LCM of 722,7685
Given numbers has no common factors except 1. So, there LCM is their product i.e 5548570
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/5548570
Therefore, the GCF of Fractions 7314/722,1842/7685 is 6/5548570
Least Common Multiple of 722,7685 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 722,7685 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(722,7685) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(722,7685) x common factors =1 x 1 = 1
LCM(722,7685) = ( 722 × 7685 ) / 1
LCM(722,7685) = 5548570 / 1
LCM(722,7685) = 5548570
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FAQs on GCF of Fractions of 7314/722, 1842/7685
1. What is the HCF of 7314,1842?
The HCF of 7314,1842 is 6
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 7314/722, 1842/7685?
Answer: GCF of Numerators as per given numbers 7314/722, 1842/7685 is
GCF of Numerators i.e. for 7314,1842 is 6
LCM of denominators i.e. for 722,7685 is 5548570.
Thus, GCF of Fractions is 6/5548570.Finally, GCF of Fractions for 7314/722, 1842/7685 is 6/5548570.