GCF of 864/14, 360/265
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 864/14, 360/265 i.e 72/3710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 864/14, 360/265.
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 864/14,360/265?
Given fractions are 864/14,360/265
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 864/14,360/265, numerators are 864,360
Denominators are 14,265
The GCF of 864,360 is 72 .
LCM of 14,265 is 3710.
The greatest common factor of 864/14,360/265 = [GCF of 864,360]/[LCM of 14,265]= 72/3710
Therefore, the GCF of 864/14,360/265 is 72/3710.
To find the highest common factor of 864,360, we have to find the factors of both numbers and list the highest common factor.
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The HCF of 864,360 is 72.
Lets's calculate GCF of 864,360
| 2 | 864, 360 |
| 2 | 432, 180 |
| 2 | 216, 90 |
| 3 | 108, 45 |
| 3 | 36, 15 |
| 12, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 3 = 72
Greatest Common Factor of 864,360 By Matching Biggest Common Factor Method
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Greatest Common Factor
We found the factors 864,360 . The biggest common factor number is the GCF number.
So the greatest common factor 864,360 is 72.
Lets's calculate LCM of 14,265
Given numbers has no common factors except 1. So, there LCM is their product i.e 3710
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 72/3710
Therefore, the GCF of Fractions 864/14,360/265 is 72/3710
Least Common Multiple of 14,265 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 14,265 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,265) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(14,265) x common factors =1 x 1 = 1
LCM(14,265) = ( 14 × 265 ) / 1
LCM(14,265) = 3710 / 1
LCM(14,265) = 3710
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FAQs on GCF of Fractions of 864/14, 360/265
1. What is the HCF of 864,360?
The HCF of 864,360 is 72
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 864/14, 360/265?
Answer: GCF of Numerators as per given numbers 864/14, 360/265 is
GCF of Numerators i.e. for 864,360 is 72
LCM of denominators i.e. for 14,265 is 3710.
Thus, GCF of Fractions is 72/3710.Finally, GCF of Fractions for 864/14, 360/265 is 72/3710.