GCF of 288/40, 160/6664
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 288/40, 160/6664 i.e 32/33320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/40, 160/6664.
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 288/40,160/6664?
Given fractions are 288/40,160/6664
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 288/40,160/6664, numerators are 288,160
Denominators are 40,6664
The GCF of 288,160 is 32 .
LCM of 40,6664 is 33320.
The greatest common factor of 288/40,160/6664 = [GCF of 288,160]/[LCM of 40,6664]= 32/33320
Therefore, the GCF of 288/40,160/6664 is 32/33320.
To find the highest common factor of 288,160, we have to find the factors of both numbers and list the highest common factor.
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The HCF of 288,160 is 32.
Lets's calculate GCF of 288,160
| 2 | 288, 160 |
| 2 | 144, 80 |
| 2 | 72, 40 |
| 2 | 36, 20 |
| 2 | 18, 10 |
| 9, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 288,160 By Matching Biggest Common Factor Method
Now, list down the factors of 288
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Greatest Common Factor
We found the factors 288,160 . The biggest common factor number is the GCF number.
So the greatest common factor 288,160 is 32.
Lets's calculate LCM of 40,6664
| 2 | 40, 6664 |
| 2 | 20, 3332 |
| 2 | 10, 1666 |
| 5, 833 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 833 = 33320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/33320
Therefore, the GCF of Fractions 288/40,160/6664 is 32/33320
Least Common Multiple of 40,6664 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 40,6664 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,6664) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(40,6664) x common factors =8 x 1 = 8
LCM(40,6664) = ( 40 × 6664 ) / 8
LCM(40,6664) = 266560 / 8
LCM(40,6664) = 33320
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FAQs on GCF of Fractions of 288/40, 160/6664
1. What is the HCF of 288,160?
The HCF of 288,160 is 32
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 288/40, 160/6664?
Answer: GCF of Numerators as per given numbers 288/40, 160/6664 is
GCF of Numerators i.e. for 288,160 is 32
LCM of denominators i.e. for 40,6664 is 33320.
Thus, GCF of Fractions is 32/33320.Finally, GCF of Fractions for 288/40, 160/6664 is 32/33320.