GCF of 5442/827, 6784/5284
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5442/827, 6784/5284 i.e 2/4369868 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5442/827, 6784/5284.
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 5442/827,6784/5284?
Given fractions are 5442/827,6784/5284
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 5442/827,6784/5284, numerators are 5442,6784
Denominators are 827,5284
The GCF of 5442,6784 is 2 .
LCM of 827,5284 is 4369868.
The greatest common factor of 5442/827,6784/5284 = [GCF of 5442,6784]/[LCM of 827,5284]= 2/4369868
Therefore, the GCF of 5442/827,6784/5284 is 2/4369868.
To find the highest common factor of 5442,6784, we have to find the factors of both numbers and list the highest common factor.
The factors of 5442 are 1, 2, 3, 6, 907, 1814, 2721, 5442
The factors of 6784 are 1, 2, 4, 8, 16, 32, 53, 64, 106, 128, 212, 424, 848, 1696, 3392, 6784
The HCF of 5442,6784 is 2.
Lets's calculate GCF of 5442,6784
| 2 | 5442, 6784 |
| 2721, 3392 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 5442,6784 By Matching Biggest Common Factor Method
Now, list down the factors of 5442
:1,2,3,6,907,1814,2721,5442
Now, list down the factors of 6784
:1,2,4,8,16,32,53,64,106,128,212,424,848,1696,3392,6784
Greatest Common Factor
We found the factors 5442,6784 . The biggest common factor number is the GCF number.
So the greatest common factor 5442,6784 is 2.
Lets's calculate LCM of 827,5284
Given numbers has no common factors except 1. So, there LCM is their product i.e 4369868
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4369868
Therefore, the GCF of Fractions 5442/827,6784/5284 is 2/4369868
Least Common Multiple of 827,5284 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 827,5284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(827,5284) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(827,5284) x common factors =1 x 1 = 1
LCM(827,5284) = ( 827 × 5284 ) / 1
LCM(827,5284) = 4369868 / 1
LCM(827,5284) = 4369868
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FAQs on GCF of Fractions of 5442/827, 6784/5284
1. What is the HCF of 5442,6784?
The HCF of 5442,6784 is 2
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 5442/827, 6784/5284?
Answer: GCF of Numerators as per given numbers 5442/827, 6784/5284 is
GCF of Numerators i.e. for 5442,6784 is 2
LCM of denominators i.e. for 827,5284 is 4369868.
Thus, GCF of Fractions is 2/4369868.Finally, GCF of Fractions for 5442/827, 6784/5284 is 2/4369868.