GCF of 237/654, 728/109
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 237/654, 728/109 i.e 1/654 easily. The following is the detailed procedure to determine the greatest common factor of fractions 237/654, 728/109.
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 237/654,728/109?
Given fractions are 237/654,728/109
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 237/654,728/109, numerators are 237,728
Denominators are 654,109
The GCF of 237,728 is 1 .
LCM of 654,109 is 654.
The greatest common factor of 237/654,728/109 = [GCF of 237,728]/[LCM of 654,109]= 1/654
Therefore, the GCF of 237/654,728/109 is 1/654.
To find the highest common factor of 237,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 237 are 1, 3, 79, 237
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 237,728 is 1.
Lets's calculate GCF of 237,728
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 237,728 By Matching Biggest Common Factor Method
Now, list down the factors of 237
:1,3,79,237
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 237,728 . The biggest common factor number is the GCF number.
So the greatest common factor 237,728 is 1.
Lets's calculate LCM of 654,109
| 109 | 654, 109 |
| 6, 1 |
∴ So the LCM of the given numbers is 109 x 6 x 1 = 654
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/654
Therefore, the GCF of Fractions 237/654,728/109 is 1/654
Least Common Multiple of 654,109 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 654,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(654,109) = 109
common factors(in case of two or more numbers have common factors) = 1
GCF(654,109) x common factors =109 x 1 = 109
LCM(654,109) = ( 654 × 109 ) / 109
LCM(654,109) = 71286 / 109
LCM(654,109) = 654
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FAQs on GCF of Fractions of 237/654, 728/109
1. What is the HCF of 237,728?
The HCF of 237,728 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 237/654, 728/109?
Answer: GCF of Numerators as per given numbers 237/654, 728/109 is
GCF of Numerators i.e. for 237,728 is 1
LCM of denominators i.e. for 654,109 is 654.
Thus, GCF of Fractions is 1/654.Finally, GCF of Fractions for 237/654, 728/109 is 1/654.