GCF of 5612/240, 7696/3514
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5612/240, 7696/3514 i.e 4/421680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5612/240, 7696/3514.
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 5612/240,7696/3514?
Given fractions are 5612/240,7696/3514
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 5612/240,7696/3514, numerators are 5612,7696
Denominators are 240,3514
The GCF of 5612,7696 is 4 .
LCM of 240,3514 is 421680.
The greatest common factor of 5612/240,7696/3514 = [GCF of 5612,7696]/[LCM of 240,3514]= 4/421680
Therefore, the GCF of 5612/240,7696/3514 is 4/421680.
To find the highest common factor of 5612,7696, we have to find the factors of both numbers and list the highest common factor.
The factors of 5612 are 1, 2, 4, 23, 46, 61, 92, 122, 244, 1403, 2806, 5612
The factors of 7696 are 1, 2, 4, 8, 13, 16, 26, 37, 52, 74, 104, 148, 208, 296, 481, 592, 962, 1924, 3848, 7696
The HCF of 5612,7696 is 4.
Lets's calculate GCF of 5612,7696
| 2 | 5612, 7696 |
| 2 | 2806, 3848 |
| 1403, 1924 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 5612,7696 By Matching Biggest Common Factor Method
Now, list down the factors of 5612
:1,2,4,23,46,61,92,122,244,1403,2806,5612
Now, list down the factors of 7696
:1,2,4,8,13,16,26,37,52,74,104,148,208,296,481,592,962,1924,3848,7696
Greatest Common Factor
We found the factors 5612,7696 . The biggest common factor number is the GCF number.
So the greatest common factor 5612,7696 is 4.
Lets's calculate LCM of 240,3514
| 2 | 240, 3514 |
| 120, 1757 |
∴ So the LCM of the given numbers is 2 x 120 x 1757 = 421680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/421680
Therefore, the GCF of Fractions 5612/240,7696/3514 is 4/421680
Least Common Multiple of 240,3514 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 240,3514 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(240,3514) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(240,3514) x common factors =2 x 1 = 2
LCM(240,3514) = ( 240 × 3514 ) / 2
LCM(240,3514) = 843360 / 2
LCM(240,3514) = 421680
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FAQs on GCF of Fractions of 5612/240, 7696/3514
1. What is the HCF of 5612,7696?
The HCF of 5612,7696 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 5612/240, 7696/3514?
Answer: GCF of Numerators as per given numbers 5612/240, 7696/3514 is
GCF of Numerators i.e. for 5612,7696 is 4
LCM of denominators i.e. for 240,3514 is 421680.
Thus, GCF of Fractions is 4/421680.Finally, GCF of Fractions for 5612/240, 7696/3514 is 4/421680.