GCF of 1965/360, 2205/8320
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1965/360, 2205/8320 i.e 15/74880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1965/360, 2205/8320.
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 1965/360,2205/8320?
Given fractions are 1965/360,2205/8320
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 1965/360,2205/8320, numerators are 1965,2205
Denominators are 360,8320
The GCF of 1965,2205 is 15 .
LCM of 360,8320 is 74880.
The greatest common factor of 1965/360,2205/8320 = [GCF of 1965,2205]/[LCM of 360,8320]= 15/74880
Therefore, the GCF of 1965/360,2205/8320 is 15/74880.
To find the highest common factor of 1965,2205, we have to find the factors of both numbers and list the highest common factor.
The factors of 1965 are 1, 3, 5, 15, 131, 393, 655, 1965
The factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205
The HCF of 1965,2205 is 15.
Lets's calculate GCF of 1965,2205
| 3 | 1965, 2205 |
| 5 | 655, 735 |
| 131, 147 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 1965,2205 By Matching Biggest Common Factor Method
Now, list down the factors of 1965
:1,3,5,15,131,393,655,1965
Now, list down the factors of 2205
:1,3,5,7,9,15,21,35,45,49,63,105,147,245,315,441,735,2205
Greatest Common Factor
We found the factors 1965,2205 . The biggest common factor number is the GCF number.
So the greatest common factor 1965,2205 is 15.
Lets's calculate LCM of 360,8320
| 2 | 360, 8320 |
| 2 | 180, 4160 |
| 2 | 90, 2080 |
| 5 | 45, 1040 |
| 9, 208 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 9 x 208 = 74880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/74880
Therefore, the GCF of Fractions 1965/360,2205/8320 is 15/74880
Least Common Multiple of 360,8320 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 360,8320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(360,8320) = 40
common factors(in case of two or more numbers have common factors) = 1
GCF(360,8320) x common factors =40 x 1 = 40
LCM(360,8320) = ( 360 × 8320 ) / 40
LCM(360,8320) = 2995200 / 40
LCM(360,8320) = 74880
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FAQs on GCF of Fractions of 1965/360, 2205/8320
1. What is the HCF of 1965,2205?
The HCF of 1965,2205 is 15
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 1965/360, 2205/8320?
Answer: GCF of Numerators as per given numbers 1965/360, 2205/8320 is
GCF of Numerators i.e. for 1965,2205 is 15
LCM of denominators i.e. for 360,8320 is 74880.
Thus, GCF of Fractions is 15/74880.Finally, GCF of Fractions for 1965/360, 2205/8320 is 15/74880.