GCF of 1600/306, 7995/144
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1600/306, 7995/144 i.e 5/2448 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1600/306, 7995/144.
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 1600/306,7995/144?
Given fractions are 1600/306,7995/144
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 1600/306,7995/144, numerators are 1600,7995
Denominators are 306,144
The GCF of 1600,7995 is 5 .
LCM of 306,144 is 2448.
The greatest common factor of 1600/306,7995/144 = [GCF of 1600,7995]/[LCM of 306,144]= 5/2448
Therefore, the GCF of 1600/306,7995/144 is 5/2448.
To find the highest common factor of 1600,7995, we have to find the factors of both numbers and list the highest common factor.
The factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600
The factors of 7995 are 1, 3, 5, 13, 15, 39, 41, 65, 123, 195, 205, 533, 615, 1599, 2665, 7995
The HCF of 1600,7995 is 5.
Lets's calculate GCF of 1600,7995
| 5 | 1600, 7995 |
| 320, 1599 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 1600,7995 By Matching Biggest Common Factor Method
Now, list down the factors of 1600
:1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800,1600
Now, list down the factors of 7995
:1,3,5,13,15,39,41,65,123,195,205,533,615,1599,2665,7995
Greatest Common Factor
We found the factors 1600,7995 . The biggest common factor number is the GCF number.
So the greatest common factor 1600,7995 is 5.
Lets's calculate LCM of 306,144
| 2 | 306, 144 |
| 3 | 153, 72 |
| 3 | 51, 24 |
| 17, 8 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 17 x 8 = 2448
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/2448
Therefore, the GCF of Fractions 1600/306,7995/144 is 5/2448
Least Common Multiple of 306,144 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 306,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,144) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(306,144) x common factors =18 x 1 = 18
LCM(306,144) = ( 306 × 144 ) / 18
LCM(306,144) = 44064 / 18
LCM(306,144) = 2448
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FAQs on GCF of Fractions of 1600/306, 7995/144
1. What is the HCF of 1600,7995?
The HCF of 1600,7995 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 1600/306, 7995/144?
Answer: GCF of Numerators as per given numbers 1600/306, 7995/144 is
GCF of Numerators i.e. for 1600,7995 is 5
LCM of denominators i.e. for 306,144 is 2448.
Thus, GCF of Fractions is 5/2448.Finally, GCF of Fractions for 1600/306, 7995/144 is 5/2448.