GCF of 323/65, 442/200
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 323/65, 442/200 i.e 17/2600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 323/65, 442/200.
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 323/65,442/200?
Given fractions are 323/65,442/200
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 323/65,442/200, numerators are 323,442
Denominators are 65,200
The GCF of 323,442 is 17 .
LCM of 65,200 is 2600.
The greatest common factor of 323/65,442/200 = [GCF of 323,442]/[LCM of 65,200]= 17/2600
Therefore, the GCF of 323/65,442/200 is 17/2600.
To find the highest common factor of 323,442, we have to find the factors of both numbers and list the highest common factor.
The factors of 323 are 1, 17, 19, 323
The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442
The HCF of 323,442 is 17.
Lets's calculate GCF of 323,442
| 17 | 323, 442 |
| 19, 26 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 323,442 By Matching Biggest Common Factor Method
Now, list down the factors of 323
:1,17,19,323
Now, list down the factors of 442
:1,2,13,17,26,34,221,442
Greatest Common Factor
We found the factors 323,442 . The biggest common factor number is the GCF number.
So the greatest common factor 323,442 is 17.
Lets's calculate LCM of 65,200
| 5 | 65, 200 |
| 13, 40 |
∴ So the LCM of the given numbers is 5 x 13 x 40 = 2600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/2600
Therefore, the GCF of Fractions 323/65,442/200 is 17/2600
Least Common Multiple of 65,200 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 65,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,200) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(65,200) x common factors =5 x 1 = 5
LCM(65,200) = ( 65 × 200 ) / 5
LCM(65,200) = 13000 / 5
LCM(65,200) = 2600
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FAQs on GCF of Fractions of 323/65, 442/200
1. What is the HCF of 323,442?
The HCF of 323,442 is 17
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 323/65, 442/200?
Answer: GCF of Numerators as per given numbers 323/65, 442/200 is
GCF of Numerators i.e. for 323,442 is 17
LCM of denominators i.e. for 65,200 is 2600.
Thus, GCF of Fractions is 17/2600.Finally, GCF of Fractions for 323/65, 442/200 is 17/2600.