GCF of 289/30, 740/916
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 289/30, 740/916 i.e 1/13740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 289/30, 740/916.
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 289/30,740/916?
Given fractions are 289/30,740/916
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 289/30,740/916, numerators are 289,740
Denominators are 30,916
The GCF of 289,740 is 1 .
LCM of 30,916 is 13740.
The greatest common factor of 289/30,740/916 = [GCF of 289,740]/[LCM of 30,916]= 1/13740
Therefore, the GCF of 289/30,740/916 is 1/13740.
To find the highest common factor of 289,740, we have to find the factors of both numbers and list the highest common factor.
The factors of 289 are 1, 17, 289
The factors of 740 are 1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740
The HCF of 289,740 is 1.
Lets's calculate GCF of 289,740
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 289,740 By Matching Biggest Common Factor Method
Now, list down the factors of 289
:1,17,289
Now, list down the factors of 740
:1,2,4,5,10,20,37,74,148,185,370,740
Greatest Common Factor
We found the factors 289,740 . The biggest common factor number is the GCF number.
So the greatest common factor 289,740 is 1.
Lets's calculate LCM of 30,916
| 2 | 30, 916 |
| 15, 458 |
∴ So the LCM of the given numbers is 2 x 15 x 458 = 13740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13740
Therefore, the GCF of Fractions 289/30,740/916 is 1/13740
Least Common Multiple of 30,916 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 30,916 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,916) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(30,916) x common factors =2 x 1 = 2
LCM(30,916) = ( 30 × 916 ) / 2
LCM(30,916) = 27480 / 2
LCM(30,916) = 13740
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FAQs on GCF of Fractions of 289/30, 740/916
1. What is the HCF of 289,740?
The HCF of 289,740 is 1
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 289/30, 740/916?
Answer: GCF of Numerators as per given numbers 289/30, 740/916 is
GCF of Numerators i.e. for 289,740 is 1
LCM of denominators i.e. for 30,916 is 13740.
Thus, GCF of Fractions is 1/13740.Finally, GCF of Fractions for 289/30, 740/916 is 1/13740.