GCF of 1713/284, 6816/9572
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1713/284, 6816/9572 i.e 3/679612 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1713/284, 6816/9572.
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 1713/284,6816/9572?
Given fractions are 1713/284,6816/9572
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 1713/284,6816/9572, numerators are 1713,6816
Denominators are 284,9572
The GCF of 1713,6816 is 3 .
LCM of 284,9572 is 679612.
The greatest common factor of 1713/284,6816/9572 = [GCF of 1713,6816]/[LCM of 284,9572]= 3/679612
Therefore, the GCF of 1713/284,6816/9572 is 3/679612.
To find the highest common factor of 1713,6816, we have to find the factors of both numbers and list the highest common factor.
The factors of 1713 are 1, 3, 571, 1713
The factors of 6816 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 71, 96, 142, 213, 284, 426, 568, 852, 1136, 1704, 2272, 3408, 6816
The HCF of 1713,6816 is 3.
Lets's calculate GCF of 1713,6816
| 3 | 1713, 6816 |
| 571, 2272 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1713,6816 By Matching Biggest Common Factor Method
Now, list down the factors of 1713
:1,3,571,1713
Now, list down the factors of 6816
:1,2,3,4,6,8,12,16,24,32,48,71,96,142,213,284,426,568,852,1136,1704,2272,3408,6816
Greatest Common Factor
We found the factors 1713,6816 . The biggest common factor number is the GCF number.
So the greatest common factor 1713,6816 is 3.
Lets's calculate LCM of 284,9572
| 2 | 284, 9572 |
| 2 | 142, 4786 |
| 71, 2393 |
∴ So the LCM of the given numbers is 2 x 2 x 71 x 2393 = 679612
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/679612
Therefore, the GCF of Fractions 1713/284,6816/9572 is 3/679612
Least Common Multiple of 284,9572 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 284,9572 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(284,9572) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(284,9572) x common factors =4 x 1 = 4
LCM(284,9572) = ( 284 × 9572 ) / 4
LCM(284,9572) = 2718448 / 4
LCM(284,9572) = 679612
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FAQs on GCF of Fractions of 1713/284, 6816/9572
1. What is the HCF of 1713,6816?
The HCF of 1713,6816 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 1713/284, 6816/9572?
Answer: GCF of Numerators as per given numbers 1713/284, 6816/9572 is
GCF of Numerators i.e. for 1713,6816 is 3
LCM of denominators i.e. for 284,9572 is 679612.
Thus, GCF of Fractions is 3/679612.Finally, GCF of Fractions for 1713/284, 6816/9572 is 3/679612.