GCF of 65/30, 95/55, 945/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 65/30, 95/55, 945/978 i.e 5/53790 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/30, 95/55, 945/978.
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 65/30,95/55,945/978?
Given fractions are 65/30,95/55,945/978
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 65/30,95/55,945/978, numerators are 65,95,945
Denominators are 30,55,978
The GCF of 65,95,945 is 5 .
LCM of 30,55,978 is 53790.
The greatest common factor of 65/30,95/55,945/978 = [GCF of 65,95,945]/[LCM of 30,55,978]= 5/53790
Therefore, the GCF of 65/30,95/55,945/978 is 5/53790.
To find the highest common factor of 65,95,945, we have to find the factors of both numbers and list the highest common factor.
The factors of 65 are 1, 5, 13, 65
The factors of 95 are 1, 5, 19, 95
The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945
The HCF of 65,95,945 is 5.
Lets's calculate GCF of 65,95,945
| 5 | 65, 95, 945 |
| 13, 19, 189 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 65,95,945 By Matching Biggest Common Factor Method
Now, list down the factors of 65
:1,5,13,65
Now, list down the factors of 95
:1,5,19,95
Now, list down the factors of 945
:1,3,5,7,9,15,21,27,35,45,63,105,135,189,315,945
Greatest Common Factor
We found the factors 65,95,945 . The biggest common factor number is the GCF number.
So the greatest common factor 65,95,945 is 5.
Lets's calculate LCM of 30,55,978
| 2 | 30, 55, 978 |
| 3 | 15, 55, 489 |
| 5 | 5, 55, 163 |
| 1, 11, 163 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 1 x 11 x 163 = 53790
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/53790
Therefore, the GCF of Fractions 65/30,95/55,945/978 is 5/53790
Least Common Multiple of 30,55,978 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 30,55,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,55,978) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(30,55,978) x common factors =1 x 30 = 30
LCM(30,55,978) = ( 30 × 55 × 978 ) / 30
LCM(30,55,978) = 1613700 / 30
LCM(30,55,978) = 53790
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 65/30, 95/55, 945/978
1. What is the HCF of 65,95,945?
The HCF of 65,95,945 is 5
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 65/30, 95/55, 945/978?
Answer: GCF of Numerators as per given numbers 65/30, 95/55, 945/978 is
GCF of Numerators i.e. for 65,95,945 is 5
LCM of denominators i.e. for 30,55,978 is 53790.
Thus, GCF of Fractions is 5/53790.Finally, GCF of Fractions for 65/30, 95/55, 945/978 is 5/53790.