GCF of 5769/340, 5431/224
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5769/340, 5431/224 i.e 1/19040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5769/340, 5431/224.
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 5769/340,5431/224?
Given fractions are 5769/340,5431/224
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 5769/340,5431/224, numerators are 5769,5431
Denominators are 340,224
The GCF of 5769,5431 is 1 .
LCM of 340,224 is 19040.
The greatest common factor of 5769/340,5431/224 = [GCF of 5769,5431]/[LCM of 340,224]= 1/19040
Therefore, the GCF of 5769/340,5431/224 is 1/19040.
To find the highest common factor of 5769,5431, we have to find the factors of both numbers and list the highest common factor.
The factors of 5769 are 1, 3, 9, 641, 1923, 5769
The factors of 5431 are 1, 5431
The HCF of 5769,5431 is 1.
Lets's calculate GCF of 5769,5431
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 5769,5431 By Matching Biggest Common Factor Method
Now, list down the factors of 5769
:1,3,9,641,1923,5769
Now, list down the factors of 5431
:1,5431
Greatest Common Factor
We found the factors 5769,5431 . The biggest common factor number is the GCF number.
So the greatest common factor 5769,5431 is 1.
Lets's calculate LCM of 340,224
| 2 | 340, 224 |
| 2 | 170, 112 |
| 85, 56 |
∴ So the LCM of the given numbers is 2 x 2 x 85 x 56 = 19040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/19040
Therefore, the GCF of Fractions 5769/340,5431/224 is 1/19040
Least Common Multiple of 340,224 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 340,224 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(340,224) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(340,224) x common factors =4 x 1 = 4
LCM(340,224) = ( 340 × 224 ) / 4
LCM(340,224) = 76160 / 4
LCM(340,224) = 19040
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FAQs on GCF of Fractions of 5769/340, 5431/224
1. What is the HCF of 5769,5431?
The HCF of 5769,5431 is 1
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 5769/340, 5431/224?
Answer: GCF of Numerators as per given numbers 5769/340, 5431/224 is
GCF of Numerators i.e. for 5769,5431 is 1
LCM of denominators i.e. for 340,224 is 19040.
Thus, GCF of Fractions is 1/19040.Finally, GCF of Fractions for 5769/340, 5431/224 is 1/19040.