GCF of 233/15, 464/65, 290/78
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 233/15, 464/65, 290/78 i.e 1/390 easily. The following is the detailed procedure to determine the greatest common factor of fractions 233/15, 464/65, 290/78.
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 233/15,464/65,290/78?
Given fractions are 233/15,464/65,290/78
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 233/15,464/65,290/78, numerators are 233,464,290
Denominators are 15,65,78
The GCF of 233,464,290 is 1 .
LCM of 15,65,78 is 390.
The greatest common factor of 233/15,464/65,290/78 = [GCF of 233,464,290]/[LCM of 15,65,78]= 1/390
Therefore, the GCF of 233/15,464/65,290/78 is 1/390.
To find the highest common factor of 233,464,290, 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 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, 464
The factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290
The HCF of 233,464,290 is 1.
Lets's calculate GCF of 233,464,290
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 233,464,290 By Matching Biggest Common Factor Method
Now, list down the factors of 233
:1,233
Now, list down the factors of 464
:1,2,4,8,16,29,58,116,232,464
Now, list down the factors of 290
:1,2,5,10,29,58,145,290
Greatest Common Factor
We found the factors 233,464,290 . The biggest common factor number is the GCF number.
So the greatest common factor 233,464,290 is 1.
Lets's calculate LCM of 15,65,78
| 3 | 15, 65, 78 |
| 5 | 5, 65, 26 |
| 13 | 1, 13, 26 |
| 1, 1, 2 |
∴ So the LCM of the given numbers is 3 x 5 x 13 x 1 x 1 x 2 = 390
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/390
Therefore, the GCF of Fractions 233/15,464/65,290/78 is 1/390
Least Common Multiple of 15,65,78 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 15,65,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(15,65,78) = 1
common factors(in case of two or more numbers have common factors) = 195
GCF(15,65,78) x common factors =1 x 195 = 195
LCM(15,65,78) = ( 15 × 65 × 78 ) / 195
LCM(15,65,78) = 76050 / 195
LCM(15,65,78) = 390
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FAQs on GCF of Fractions of 233/15, 464/65, 290/78
1. What is the HCF of 233,464,290?
The HCF of 233,464,290 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 233/15, 464/65, 290/78?
Answer: GCF of Numerators as per given numbers 233/15, 464/65, 290/78 is
GCF of Numerators i.e. for 233,464,290 is 1
LCM of denominators i.e. for 15,65,78 is 390.
Thus, GCF of Fractions is 1/390.Finally, GCF of Fractions for 233/15, 464/65, 290/78 is 1/390.