GCF of 432/85, 512/576
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 432/85, 512/576 i.e 16/48960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 432/85, 512/576.
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 432/85,512/576?
Given fractions are 432/85,512/576
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 432/85,512/576, numerators are 432,512
Denominators are 85,576
The GCF of 432,512 is 16 .
LCM of 85,576 is 48960.
The greatest common factor of 432/85,512/576 = [GCF of 432,512]/[LCM of 85,576]= 16/48960
Therefore, the GCF of 432/85,512/576 is 16/48960.
To find the highest common factor of 432,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 432,512 is 16.
Lets's calculate GCF of 432,512
| 2 | 432, 512 |
| 2 | 216, 256 |
| 2 | 108, 128 |
| 2 | 54, 64 |
| 27, 32 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 432,512 By Matching Biggest Common Factor Method
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 432,512 . The biggest common factor number is the GCF number.
So the greatest common factor 432,512 is 16.
Lets's calculate LCM of 85,576
Given numbers has no common factors except 1. So, there LCM is their product i.e 48960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/48960
Therefore, the GCF of Fractions 432/85,512/576 is 16/48960
Least Common Multiple of 85,576 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 85,576 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,576) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(85,576) x common factors =1 x 1 = 1
LCM(85,576) = ( 85 × 576 ) / 1
LCM(85,576) = 48960 / 1
LCM(85,576) = 48960
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FAQs on GCF of Fractions of 432/85, 512/576
1. What is the HCF of 432,512?
The HCF of 432,512 is 16
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 432/85, 512/576?
Answer: GCF of Numerators as per given numbers 432/85, 512/576 is
GCF of Numerators i.e. for 432,512 is 16
LCM of denominators i.e. for 85,576 is 48960.
Thus, GCF of Fractions is 16/48960.Finally, GCF of Fractions for 432/85, 512/576 is 16/48960.