GCF of 2128/205, 8432/8369
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2128/205, 8432/8369 i.e 16/1715645 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2128/205, 8432/8369.
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 2128/205,8432/8369?
Given fractions are 2128/205,8432/8369
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 2128/205,8432/8369, numerators are 2128,8432
Denominators are 205,8369
The GCF of 2128,8432 is 16 .
LCM of 205,8369 is 1715645.
The greatest common factor of 2128/205,8432/8369 = [GCF of 2128,8432]/[LCM of 205,8369]= 16/1715645
Therefore, the GCF of 2128/205,8432/8369 is 16/1715645.
To find the highest common factor of 2128,8432, we have to find the factors of both numbers and list the highest common factor.
The factors of 2128 are 1, 2, 4, 7, 8, 14, 16, 19, 28, 38, 56, 76, 112, 133, 152, 266, 304, 532, 1064, 2128
The factors of 8432 are 1, 2, 4, 8, 16, 17, 31, 34, 62, 68, 124, 136, 248, 272, 496, 527, 1054, 2108, 4216, 8432
The HCF of 2128,8432 is 16.
Lets's calculate GCF of 2128,8432
| 2 | 2128, 8432 |
| 2 | 1064, 4216 |
| 2 | 532, 2108 |
| 2 | 266, 1054 |
| 133, 527 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 2128,8432 By Matching Biggest Common Factor Method
Now, list down the factors of 2128
:1,2,4,7,8,14,16,19,28,38,56,76,112,133,152,266,304,532,1064,2128
Now, list down the factors of 8432
:1,2,4,8,16,17,31,34,62,68,124,136,248,272,496,527,1054,2108,4216,8432
Greatest Common Factor
We found the factors 2128,8432 . The biggest common factor number is the GCF number.
So the greatest common factor 2128,8432 is 16.
Lets's calculate LCM of 205,8369
Given numbers has no common factors except 1. So, there LCM is their product i.e 1715645
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/1715645
Therefore, the GCF of Fractions 2128/205,8432/8369 is 16/1715645
Least Common Multiple of 205,8369 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 205,8369 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,8369) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,8369) x common factors =1 x 1 = 1
LCM(205,8369) = ( 205 × 8369 ) / 1
LCM(205,8369) = 1715645 / 1
LCM(205,8369) = 1715645
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FAQs on GCF of Fractions of 2128/205, 8432/8369
1. What is the HCF of 2128,8432?
The HCF of 2128,8432 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 2128/205, 8432/8369?
Answer: GCF of Numerators as per given numbers 2128/205, 8432/8369 is
GCF of Numerators i.e. for 2128,8432 is 16
LCM of denominators i.e. for 205,8369 is 1715645.
Thus, GCF of Fractions is 16/1715645.Finally, GCF of Fractions for 2128/205, 8432/8369 is 16/1715645.