GCF of 1649/257, 1938/4384
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1649/257, 1938/4384 i.e 17/1126688 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1649/257, 1938/4384.
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 1649/257,1938/4384?
Given fractions are 1649/257,1938/4384
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 1649/257,1938/4384, numerators are 1649,1938
Denominators are 257,4384
The GCF of 1649,1938 is 17 .
LCM of 257,4384 is 1126688.
The greatest common factor of 1649/257,1938/4384 = [GCF of 1649,1938]/[LCM of 257,4384]= 17/1126688
Therefore, the GCF of 1649/257,1938/4384 is 17/1126688.
To find the highest common factor of 1649,1938, we have to find the factors of both numbers and list the highest common factor.
The factors of 1649 are 1, 17, 97, 1649
The factors of 1938 are 1, 2, 3, 6, 17, 19, 34, 38, 51, 57, 102, 114, 323, 646, 969, 1938
The HCF of 1649,1938 is 17.
Lets's calculate GCF of 1649,1938
| 17 | 1649, 1938 |
| 97, 114 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 1649,1938 By Matching Biggest Common Factor Method
Now, list down the factors of 1649
:1,17,97,1649
Now, list down the factors of 1938
:1,2,3,6,17,19,34,38,51,57,102,114,323,646,969,1938
Greatest Common Factor
We found the factors 1649,1938 . The biggest common factor number is the GCF number.
So the greatest common factor 1649,1938 is 17.
Lets's calculate LCM of 257,4384
Given numbers has no common factors except 1. So, there LCM is their product i.e 1126688
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/1126688
Therefore, the GCF of Fractions 1649/257,1938/4384 is 17/1126688
Least Common Multiple of 257,4384 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 257,4384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(257,4384) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(257,4384) x common factors =1 x 1 = 1
LCM(257,4384) = ( 257 × 4384 ) / 1
LCM(257,4384) = 1126688 / 1
LCM(257,4384) = 1126688
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FAQs on GCF of Fractions of 1649/257, 1938/4384
1. What is the HCF of 1649,1938?
The HCF of 1649,1938 is 17
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 1649/257, 1938/4384?
Answer: GCF of Numerators as per given numbers 1649/257, 1938/4384 is
GCF of Numerators i.e. for 1649,1938 is 17
LCM of denominators i.e. for 257,4384 is 1126688.
Thus, GCF of Fractions is 17/1126688.Finally, GCF of Fractions for 1649/257, 1938/4384 is 17/1126688.