GCF of 5469/564, 8034/288
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5469/564, 8034/288 i.e 3/13536 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5469/564, 8034/288.
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 5469/564,8034/288?
Given fractions are 5469/564,8034/288
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 5469/564,8034/288, numerators are 5469,8034
Denominators are 564,288
The GCF of 5469,8034 is 3 .
LCM of 564,288 is 13536.
The greatest common factor of 5469/564,8034/288 = [GCF of 5469,8034]/[LCM of 564,288]= 3/13536
Therefore, the GCF of 5469/564,8034/288 is 3/13536.
To find the highest common factor of 5469,8034, we have to find the factors of both numbers and list the highest common factor.
The factors of 5469 are 1, 3, 1823, 5469
The factors of 8034 are 1, 2, 3, 6, 13, 26, 39, 78, 103, 206, 309, 618, 1339, 2678, 4017, 8034
The HCF of 5469,8034 is 3.
Lets's calculate GCF of 5469,8034
| 3 | 5469, 8034 |
| 1823, 2678 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 5469,8034 By Matching Biggest Common Factor Method
Now, list down the factors of 5469
:1,3,1823,5469
Now, list down the factors of 8034
:1,2,3,6,13,26,39,78,103,206,309,618,1339,2678,4017,8034
Greatest Common Factor
We found the factors 5469,8034 . The biggest common factor number is the GCF number.
So the greatest common factor 5469,8034 is 3.
Lets's calculate LCM of 564,288
| 2 | 564, 288 |
| 2 | 282, 144 |
| 3 | 141, 72 |
| 47, 24 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 47 x 24 = 13536
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/13536
Therefore, the GCF of Fractions 5469/564,8034/288 is 3/13536
Least Common Multiple of 564,288 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 564,288 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,288) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(564,288) x common factors =12 x 1 = 12
LCM(564,288) = ( 564 × 288 ) / 12
LCM(564,288) = 162432 / 12
LCM(564,288) = 13536
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FAQs on GCF of Fractions of 5469/564, 8034/288
1. What is the HCF of 5469,8034?
The HCF of 5469,8034 is 3
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 5469/564, 8034/288?
Answer: GCF of Numerators as per given numbers 5469/564, 8034/288 is
GCF of Numerators i.e. for 5469,8034 is 3
LCM of denominators i.e. for 564,288 is 13536.
Thus, GCF of Fractions is 3/13536.Finally, GCF of Fractions for 5469/564, 8034/288 is 3/13536.