GCF of 2116/264, 3136/7744
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2116/264, 3136/7744 i.e 4/23232 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2116/264, 3136/7744.
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 2116/264,3136/7744?
Given fractions are 2116/264,3136/7744
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 2116/264,3136/7744, numerators are 2116,3136
Denominators are 264,7744
The GCF of 2116,3136 is 4 .
LCM of 264,7744 is 23232.
The greatest common factor of 2116/264,3136/7744 = [GCF of 2116,3136]/[LCM of 264,7744]= 4/23232
Therefore, the GCF of 2116/264,3136/7744 is 4/23232.
To find the highest common factor of 2116,3136, we have to find the factors of both numbers and list the highest common factor.
The factors of 2116 are 1, 2, 4, 23, 46, 92, 529, 1058, 2116
The factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136
The HCF of 2116,3136 is 4.
Lets's calculate GCF of 2116,3136
| 2 | 2116, 3136 |
| 2 | 1058, 1568 |
| 529, 784 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 2116,3136 By Matching Biggest Common Factor Method
Now, list down the factors of 2116
:1,2,4,23,46,92,529,1058,2116
Now, list down the factors of 3136
:1,2,4,7,8,14,16,28,32,49,56,64,98,112,196,224,392,448,784,1568,3136
Greatest Common Factor
We found the factors 2116,3136 . The biggest common factor number is the GCF number.
So the greatest common factor 2116,3136 is 4.
Lets's calculate LCM of 264,7744
| 2 | 264, 7744 |
| 2 | 132, 3872 |
| 2 | 66, 1936 |
| 11 | 33, 968 |
| 3, 88 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 11 x 3 x 88 = 23232
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/23232
Therefore, the GCF of Fractions 2116/264,3136/7744 is 4/23232
Least Common Multiple of 264,7744 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 264,7744 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(264,7744) = 88
common factors(in case of two or more numbers have common factors) = 1
GCF(264,7744) x common factors =88 x 1 = 88
LCM(264,7744) = ( 264 × 7744 ) / 88
LCM(264,7744) = 2044416 / 88
LCM(264,7744) = 23232
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FAQs on GCF of Fractions of 2116/264, 3136/7744
1. What is the HCF of 2116,3136?
The HCF of 2116,3136 is 4
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 2116/264, 3136/7744?
Answer: GCF of Numerators as per given numbers 2116/264, 3136/7744 is
GCF of Numerators i.e. for 2116,3136 is 4
LCM of denominators i.e. for 264,7744 is 23232.
Thus, GCF of Fractions is 4/23232.Finally, GCF of Fractions for 2116/264, 3136/7744 is 4/23232.