GCF of 1604/288, 1746/8134
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1604/288, 1746/8134 i.e 2/1171296 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1604/288, 1746/8134.
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 1604/288,1746/8134?
Given fractions are 1604/288,1746/8134
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 1604/288,1746/8134, numerators are 1604,1746
Denominators are 288,8134
The GCF of 1604,1746 is 2 .
LCM of 288,8134 is 1171296.
The greatest common factor of 1604/288,1746/8134 = [GCF of 1604,1746]/[LCM of 288,8134]= 2/1171296
Therefore, the GCF of 1604/288,1746/8134 is 2/1171296.
To find the highest common factor of 1604,1746, we have to find the factors of both numbers and list the highest common factor.
The factors of 1604 are 1, 2, 4, 401, 802, 1604
The factors of 1746 are 1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746
The HCF of 1604,1746 is 2.
Lets's calculate GCF of 1604,1746
| 2 | 1604, 1746 |
| 802, 873 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1604,1746 By Matching Biggest Common Factor Method
Now, list down the factors of 1604
:1,2,4,401,802,1604
Now, list down the factors of 1746
:1,2,3,6,9,18,97,194,291,582,873,1746
Greatest Common Factor
We found the factors 1604,1746 . The biggest common factor number is the GCF number.
So the greatest common factor 1604,1746 is 2.
Lets's calculate LCM of 288,8134
| 2 | 288, 8134 |
| 144, 4067 |
∴ So the LCM of the given numbers is 2 x 144 x 4067 = 1171296
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1171296
Therefore, the GCF of Fractions 1604/288,1746/8134 is 2/1171296
Least Common Multiple of 288,8134 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 288,8134 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(288,8134) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(288,8134) x common factors =2 x 1 = 2
LCM(288,8134) = ( 288 × 8134 ) / 2
LCM(288,8134) = 2342592 / 2
LCM(288,8134) = 1171296
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FAQs on GCF of Fractions of 1604/288, 1746/8134
1. What is the HCF of 1604,1746?
The HCF of 1604,1746 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 1604/288, 1746/8134?
Answer: GCF of Numerators as per given numbers 1604/288, 1746/8134 is
GCF of Numerators i.e. for 1604,1746 is 2
LCM of denominators i.e. for 288,8134 is 1171296.
Thus, GCF of Fractions is 2/1171296.Finally, GCF of Fractions for 1604/288, 1746/8134 is 2/1171296.