GCF of 533/189, 7872/1106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 533/189, 7872/1106 i.e 41/29862 easily. The following is the detailed procedure to determine the greatest common factor of fractions 533/189, 7872/1106.
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 533/189,7872/1106?
Given fractions are 533/189,7872/1106
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 533/189,7872/1106, numerators are 533,7872
Denominators are 189,1106
The GCF of 533,7872 is 41 .
LCM of 189,1106 is 29862.
The greatest common factor of 533/189,7872/1106 = [GCF of 533,7872]/[LCM of 189,1106]= 41/29862
Therefore, the GCF of 533/189,7872/1106 is 41/29862.
To find the highest common factor of 533,7872, we have to find the factors of both numbers and list the highest common factor.
The factors of 533 are 1, 13, 41, 533
The factors of 7872 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 41, 48, 64, 82, 96, 123, 164, 192, 246, 328, 492, 656, 984, 1312, 1968, 2624, 3936, 7872
The HCF of 533,7872 is 41.
Lets's calculate GCF of 533,7872
| 41 | 533, 7872 |
| 13, 192 |
∴ So the GCF of the given numbers is 41 = 41
Greatest Common Factor of 533,7872 By Matching Biggest Common Factor Method
Now, list down the factors of 533
:1,13,41,533
Now, list down the factors of 7872
:1,2,3,4,6,8,12,16,24,32,41,48,64,82,96,123,164,192,246,328,492,656,984,1312,1968,2624,3936,7872
Greatest Common Factor
We found the factors 533,7872 . The biggest common factor number is the GCF number.
So the greatest common factor 533,7872 is 41.
Lets's calculate LCM of 189,1106
| 7 | 189, 1106 |
| 27, 158 |
∴ So the LCM of the given numbers is 7 x 27 x 158 = 29862
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 41/29862
Therefore, the GCF of Fractions 533/189,7872/1106 is 41/29862
Least Common Multiple of 189,1106 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 189,1106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(189,1106) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(189,1106) x common factors =7 x 1 = 7
LCM(189,1106) = ( 189 × 1106 ) / 7
LCM(189,1106) = 209034 / 7
LCM(189,1106) = 29862
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FAQs on GCF of Fractions of 533/189, 7872/1106
1. What is the HCF of 533,7872?
The HCF of 533,7872 is 41
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 533/189, 7872/1106?
Answer: GCF of Numerators as per given numbers 533/189, 7872/1106 is
GCF of Numerators i.e. for 533,7872 is 41
LCM of denominators i.e. for 189,1106 is 29862.
Thus, GCF of Fractions is 41/29862.Finally, GCF of Fractions for 533/189, 7872/1106 is 41/29862.