GCF of 3204/381, 3430/8086
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3204/381, 3430/8086 i.e 2/3080766 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3204/381, 3430/8086.
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 3204/381,3430/8086?
Given fractions are 3204/381,3430/8086
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 3204/381,3430/8086, numerators are 3204,3430
Denominators are 381,8086
The GCF of 3204,3430 is 2 .
LCM of 381,8086 is 3080766.
The greatest common factor of 3204/381,3430/8086 = [GCF of 3204,3430]/[LCM of 381,8086]= 2/3080766
Therefore, the GCF of 3204/381,3430/8086 is 2/3080766.
To find the highest common factor of 3204,3430, we have to find the factors of both numbers and list the highest common factor.
The factors of 3204 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 89, 178, 267, 356, 534, 801, 1068, 1602, 3204
The factors of 3430 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 343, 490, 686, 1715, 3430
The HCF of 3204,3430 is 2.
Lets's calculate GCF of 3204,3430
| 2 | 3204, 3430 |
| 1602, 1715 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 3204,3430 By Matching Biggest Common Factor Method
Now, list down the factors of 3204
:1,2,3,4,6,9,12,18,36,89,178,267,356,534,801,1068,1602,3204
Now, list down the factors of 3430
:1,2,5,7,10,14,35,49,70,98,245,343,490,686,1715,3430
Greatest Common Factor
We found the factors 3204,3430 . The biggest common factor number is the GCF number.
So the greatest common factor 3204,3430 is 2.
Lets's calculate LCM of 381,8086
Given numbers has no common factors except 1. So, there LCM is their product i.e 3080766
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3080766
Therefore, the GCF of Fractions 3204/381,3430/8086 is 2/3080766
Least Common Multiple of 381,8086 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 381,8086 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(381,8086) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(381,8086) x common factors =1 x 1 = 1
LCM(381,8086) = ( 381 × 8086 ) / 1
LCM(381,8086) = 3080766 / 1
LCM(381,8086) = 3080766
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FAQs on GCF of Fractions of 3204/381, 3430/8086
1. What is the HCF of 3204,3430?
The HCF of 3204,3430 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 3204/381, 3430/8086?
Answer: GCF of Numerators as per given numbers 3204/381, 3430/8086 is
GCF of Numerators i.e. for 3204,3430 is 2
LCM of denominators i.e. for 381,8086 is 3080766.
Thus, GCF of Fractions is 2/3080766.Finally, GCF of Fractions for 3204/381, 3430/8086 is 2/3080766.