GCF of 233/213, 994/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 233/213, 994/978 i.e 1/69438 easily. The following is the detailed procedure to determine the greatest common factor of fractions 233/213, 994/978.
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 233/213,994/978?
Given fractions are 233/213,994/978
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 233/213,994/978, numerators are 233,994
Denominators are 213,978
The GCF of 233,994 is 1 .
LCM of 213,978 is 69438.
The greatest common factor of 233/213,994/978 = [GCF of 233,994]/[LCM of 213,978]= 1/69438
Therefore, the GCF of 233/213,994/978 is 1/69438.
To find the highest common factor of 233,994, we have to find the factors of both numbers and list the highest common factor.
The factors of 233 are 1, 233
The factors of 994 are 1, 2, 7, 14, 71, 142, 497, 994
The HCF of 233,994 is 1.
Lets's calculate GCF of 233,994
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 233,994 By Matching Biggest Common Factor Method
Now, list down the factors of 233
:1,233
Now, list down the factors of 994
:1,2,7,14,71,142,497,994
Greatest Common Factor
We found the factors 233,994 . The biggest common factor number is the GCF number.
So the greatest common factor 233,994 is 1.
Lets's calculate LCM of 213,978
| 3 | 213, 978 |
| 71, 326 |
∴ So the LCM of the given numbers is 3 x 71 x 326 = 69438
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/69438
Therefore, the GCF of Fractions 233/213,994/978 is 1/69438
Least Common Multiple of 213,978 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 213,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(213,978) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(213,978) x common factors =3 x 1 = 3
LCM(213,978) = ( 213 × 978 ) / 3
LCM(213,978) = 208314 / 3
LCM(213,978) = 69438
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FAQs on GCF of Fractions of 233/213, 994/978
1. What is the HCF of 233,994?
The HCF of 233,994 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 233/213, 994/978?
Answer: GCF of Numerators as per given numbers 233/213, 994/978 is
GCF of Numerators i.e. for 233,994 is 1
LCM of denominators i.e. for 213,978 is 69438.
Thus, GCF of Fractions is 1/69438.Finally, GCF of Fractions for 233/213, 994/978 is 1/69438.