GCF of 248/29, 400/289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 248/29, 400/289 i.e 8/8381 easily. The following is the detailed procedure to determine the greatest common factor of fractions 248/29, 400/289.
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 248/29,400/289?
Given fractions are 248/29,400/289
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 248/29,400/289, numerators are 248,400
Denominators are 29,289
The GCF of 248,400 is 8 .
LCM of 29,289 is 8381.
The greatest common factor of 248/29,400/289 = [GCF of 248,400]/[LCM of 29,289]= 8/8381
Therefore, the GCF of 248/29,400/289 is 8/8381.
To find the highest common factor of 248,400, we have to find the factors of both numbers and list the highest common factor.
The factors of 248 are 1, 2, 4, 8, 31, 62, 124, 248
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 248,400 is 8.
Lets's calculate GCF of 248,400
| 2 | 248, 400 |
| 2 | 124, 200 |
| 2 | 62, 100 |
| 31, 50 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 248,400 By Matching Biggest Common Factor Method
Now, list down the factors of 248
:1,2,4,8,31,62,124,248
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 248,400 . The biggest common factor number is the GCF number.
So the greatest common factor 248,400 is 8.
Lets's calculate LCM of 29,289
Given numbers has no common factors except 1. So, there LCM is their product i.e 8381
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/8381
Therefore, the GCF of Fractions 248/29,400/289 is 8/8381
Least Common Multiple of 29,289 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 29,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,289) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(29,289) x common factors =1 x 1 = 1
LCM(29,289) = ( 29 × 289 ) / 1
LCM(29,289) = 8381 / 1
LCM(29,289) = 8381
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FAQs on GCF of Fractions of 248/29, 400/289
1. What is the HCF of 248,400?
The HCF of 248,400 is 8
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 248/29, 400/289?
Answer: GCF of Numerators as per given numbers 248/29, 400/289 is
GCF of Numerators i.e. for 248,400 is 8
LCM of denominators i.e. for 29,289 is 8381.
Thus, GCF of Fractions is 8/8381.Finally, GCF of Fractions for 248/29, 400/289 is 8/8381.