GCF of 512/83, 216/196
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 512/83, 216/196 i.e 8/16268 easily. The following is the detailed procedure to determine the greatest common factor of fractions 512/83, 216/196.
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 512/83,216/196?
Given fractions are 512/83,216/196
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 512/83,216/196, numerators are 512,216
Denominators are 83,196
The GCF of 512,216 is 8 .
LCM of 83,196 is 16268.
The greatest common factor of 512/83,216/196 = [GCF of 512,216]/[LCM of 83,196]= 8/16268
Therefore, the GCF of 512/83,216/196 is 8/16268.
To find the highest common factor of 512,216, we have to find the factors of both numbers and list the highest common factor.
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The HCF of 512,216 is 8.
Lets's calculate GCF of 512,216
| 2 | 512, 216 |
| 2 | 256, 108 |
| 2 | 128, 54 |
| 64, 27 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 512,216 By Matching Biggest Common Factor Method
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Greatest Common Factor
We found the factors 512,216 . The biggest common factor number is the GCF number.
So the greatest common factor 512,216 is 8.
Lets's calculate LCM of 83,196
Given numbers has no common factors except 1. So, there LCM is their product i.e 16268
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/16268
Therefore, the GCF of Fractions 512/83,216/196 is 8/16268
Least Common Multiple of 83,196 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 83,196 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(83,196) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(83,196) x common factors =1 x 1 = 1
LCM(83,196) = ( 83 × 196 ) / 1
LCM(83,196) = 16268 / 1
LCM(83,196) = 16268
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FAQs on GCF of Fractions of 512/83, 216/196
1. What is the HCF of 512,216?
The HCF of 512,216 is 8
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 512/83, 216/196?
Answer: GCF of Numerators as per given numbers 512/83, 216/196 is
GCF of Numerators i.e. for 512,216 is 8
LCM of denominators i.e. for 83,196 is 16268.
Thus, GCF of Fractions is 8/16268.Finally, GCF of Fractions for 512/83, 216/196 is 8/16268.