GCF of 266/289, 5754/232
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 266/289, 5754/232 i.e 14/67048 easily. The following is the detailed procedure to determine the greatest common factor of fractions 266/289, 5754/232.
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 266/289,5754/232?
Given fractions are 266/289,5754/232
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 266/289,5754/232, numerators are 266,5754
Denominators are 289,232
The GCF of 266,5754 is 14 .
LCM of 289,232 is 67048.
The greatest common factor of 266/289,5754/232 = [GCF of 266,5754]/[LCM of 289,232]= 14/67048
Therefore, the GCF of 266/289,5754/232 is 14/67048.
To find the highest common factor of 266,5754, we have to find the factors of both numbers and list the highest common factor.
The factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266
The factors of 5754 are 1, 2, 3, 6, 7, 14, 21, 42, 137, 274, 411, 822, 959, 1918, 2877, 5754
The HCF of 266,5754 is 14.
Lets's calculate GCF of 266,5754
| 2 | 266, 5754 |
| 7 | 133, 2877 |
| 19, 411 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 266,5754 By Matching Biggest Common Factor Method
Now, list down the factors of 266
:1,2,7,14,19,38,133,266
Now, list down the factors of 5754
:1,2,3,6,7,14,21,42,137,274,411,822,959,1918,2877,5754
Greatest Common Factor
We found the factors 266,5754 . The biggest common factor number is the GCF number.
So the greatest common factor 266,5754 is 14.
Lets's calculate LCM of 289,232
Given numbers has no common factors except 1. So, there LCM is their product i.e 67048
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/67048
Therefore, the GCF of Fractions 266/289,5754/232 is 14/67048
Least Common Multiple of 289,232 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 289,232 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,232) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(289,232) x common factors =1 x 1 = 1
LCM(289,232) = ( 289 × 232 ) / 1
LCM(289,232) = 67048 / 1
LCM(289,232) = 67048
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FAQs on GCF of Fractions of 266/289, 5754/232
1. What is the HCF of 266,5754?
The HCF of 266,5754 is 14
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 266/289, 5754/232?
Answer: GCF of Numerators as per given numbers 266/289, 5754/232 is
GCF of Numerators i.e. for 266,5754 is 14
LCM of denominators i.e. for 289,232 is 67048.
Thus, GCF of Fractions is 14/67048.Finally, GCF of Fractions for 266/289, 5754/232 is 14/67048.