GCF of 1738/258, 8998/1984
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1738/258, 8998/1984 i.e 22/255936 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1738/258, 8998/1984.
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 1738/258,8998/1984?
Given fractions are 1738/258,8998/1984
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 1738/258,8998/1984, numerators are 1738,8998
Denominators are 258,1984
The GCF of 1738,8998 is 22 .
LCM of 258,1984 is 255936.
The greatest common factor of 1738/258,8998/1984 = [GCF of 1738,8998]/[LCM of 258,1984]= 22/255936
Therefore, the GCF of 1738/258,8998/1984 is 22/255936.
To find the highest common factor of 1738,8998, we have to find the factors of both numbers and list the highest common factor.
The factors of 1738 are 1, 2, 11, 22, 79, 158, 869, 1738
The factors of 8998 are 1, 2, 11, 22, 409, 818, 4499, 8998
The HCF of 1738,8998 is 22.
Lets's calculate GCF of 1738,8998
| 2 | 1738, 8998 |
| 11 | 869, 4499 |
| 79, 409 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 1738,8998 By Matching Biggest Common Factor Method
Now, list down the factors of 1738
:1,2,11,22,79,158,869,1738
Now, list down the factors of 8998
:1,2,11,22,409,818,4499,8998
Greatest Common Factor
We found the factors 1738,8998 . The biggest common factor number is the GCF number.
So the greatest common factor 1738,8998 is 22.
Lets's calculate LCM of 258,1984
| 2 | 258, 1984 |
| 129, 992 |
∴ So the LCM of the given numbers is 2 x 129 x 992 = 255936
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/255936
Therefore, the GCF of Fractions 1738/258,8998/1984 is 22/255936
Least Common Multiple of 258,1984 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 258,1984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(258,1984) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(258,1984) x common factors =2 x 1 = 2
LCM(258,1984) = ( 258 × 1984 ) / 2
LCM(258,1984) = 511872 / 2
LCM(258,1984) = 255936
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FAQs on GCF of Fractions of 1738/258, 8998/1984
1. What is the HCF of 1738,8998?
The HCF of 1738,8998 is 22
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 1738/258, 8998/1984?
Answer: GCF of Numerators as per given numbers 1738/258, 8998/1984 is
GCF of Numerators i.e. for 1738,8998 is 22
LCM of denominators i.e. for 258,1984 is 255936.
Thus, GCF of Fractions is 22/255936.Finally, GCF of Fractions for 1738/258, 8998/1984 is 22/255936.