GCF of 7514/248, 5491/922
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7514/248, 5491/922 i.e 289/114328 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7514/248, 5491/922.
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 7514/248,5491/922?
Given fractions are 7514/248,5491/922
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 7514/248,5491/922, numerators are 7514,5491
Denominators are 248,922
The GCF of 7514,5491 is 289 .
LCM of 248,922 is 114328.
The greatest common factor of 7514/248,5491/922 = [GCF of 7514,5491]/[LCM of 248,922]= 289/114328
Therefore, the GCF of 7514/248,5491/922 is 289/114328.
To find the highest common factor of 7514,5491, we have to find the factors of both numbers and list the highest common factor.
The factors of 7514 are 1, 2, 13, 17, 26, 34, 221, 289, 442, 578, 3757, 7514
The factors of 5491 are 1, 17, 19, 289, 323, 5491
The HCF of 7514,5491 is 289.
Lets's calculate GCF of 7514,5491
| 17 | 7514, 5491 |
| 17 | 442, 323 |
| 26, 19 |
∴ So the GCF of the given numbers is 17 x 17 = 289
Greatest Common Factor of 7514,5491 By Matching Biggest Common Factor Method
Now, list down the factors of 7514
:1,2,13,17,26,34,221,289,442,578,3757,7514
Now, list down the factors of 5491
:1,17,19,289,323,5491
Greatest Common Factor
We found the factors 7514,5491 . The biggest common factor number is the GCF number.
So the greatest common factor 7514,5491 is 289.
Lets's calculate LCM of 248,922
| 2 | 248, 922 |
| 124, 461 |
∴ So the LCM of the given numbers is 2 x 124 x 461 = 114328
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 289/114328
Therefore, the GCF of Fractions 7514/248,5491/922 is 289/114328
Least Common Multiple of 248,922 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 248,922 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(248,922) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(248,922) x common factors =2 x 1 = 2
LCM(248,922) = ( 248 × 922 ) / 2
LCM(248,922) = 228656 / 2
LCM(248,922) = 114328
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FAQs on GCF of Fractions of 7514/248, 5491/922
1. What is the HCF of 7514,5491?
The HCF of 7514,5491 is 289
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 7514/248, 5491/922?
Answer: GCF of Numerators as per given numbers 7514/248, 5491/922 is
GCF of Numerators i.e. for 7514,5491 is 289
LCM of denominators i.e. for 248,922 is 114328.
Thus, GCF of Fractions is 289/114328.Finally, GCF of Fractions for 7514/248, 5491/922 is 289/114328.