GCF of 592/71, 512/4197
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 592/71, 512/4197 i.e 16/297987 easily. The following is the detailed procedure to determine the greatest common factor of fractions 592/71, 512/4197.
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 592/71,512/4197?
Given fractions are 592/71,512/4197
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 592/71,512/4197, numerators are 592,512
Denominators are 71,4197
The GCF of 592,512 is 16 .
LCM of 71,4197 is 297987.
The greatest common factor of 592/71,512/4197 = [GCF of 592,512]/[LCM of 71,4197]= 16/297987
Therefore, the GCF of 592/71,512/4197 is 16/297987.
To find the highest common factor of 592,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 592 are 1, 2, 4, 8, 16, 37, 74, 148, 296, 592
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 592,512 is 16.
Lets's calculate GCF of 592,512
| 2 | 592, 512 |
| 2 | 296, 256 |
| 2 | 148, 128 |
| 2 | 74, 64 |
| 37, 32 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 592,512 By Matching Biggest Common Factor Method
Now, list down the factors of 592
:1,2,4,8,16,37,74,148,296,592
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 592,512 . The biggest common factor number is the GCF number.
So the greatest common factor 592,512 is 16.
Lets's calculate LCM of 71,4197
Given numbers has no common factors except 1. So, there LCM is their product i.e 297987
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/297987
Therefore, the GCF of Fractions 592/71,512/4197 is 16/297987
Least Common Multiple of 71,4197 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 71,4197 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,4197) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,4197) x common factors =1 x 1 = 1
LCM(71,4197) = ( 71 × 4197 ) / 1
LCM(71,4197) = 297987 / 1
LCM(71,4197) = 297987
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FAQs on GCF of Fractions of 592/71, 512/4197
1. What is the HCF of 592,512?
The HCF of 592,512 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 592/71, 512/4197?
Answer: GCF of Numerators as per given numbers 592/71, 512/4197 is
GCF of Numerators i.e. for 592,512 is 16
LCM of denominators i.e. for 71,4197 is 297987.
Thus, GCF of Fractions is 16/297987.Finally, GCF of Fractions for 592/71, 512/4197 is 16/297987.