GCF of 548/13, 784/2314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 548/13, 784/2314 i.e 4/2314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 548/13, 784/2314.
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 548/13,784/2314?
Given fractions are 548/13,784/2314
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 548/13,784/2314, numerators are 548,784
Denominators are 13,2314
The GCF of 548,784 is 4 .
LCM of 13,2314 is 2314.
The greatest common factor of 548/13,784/2314 = [GCF of 548,784]/[LCM of 13,2314]= 4/2314
Therefore, the GCF of 548/13,784/2314 is 4/2314.
To find the highest common factor of 548,784, we have to find the factors of both numbers and list the highest common factor.
The factors of 548 are 1, 2, 4, 137, 274, 548
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The HCF of 548,784 is 4.
Lets's calculate GCF of 548,784
| 2 | 548, 784 |
| 2 | 274, 392 |
| 137, 196 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 548,784 By Matching Biggest Common Factor Method
Now, list down the factors of 548
:1,2,4,137,274,548
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Greatest Common Factor
We found the factors 548,784 . The biggest common factor number is the GCF number.
So the greatest common factor 548,784 is 4.
Lets's calculate LCM of 13,2314
| 13 | 13, 2314 |
| 1, 178 |
∴ So the LCM of the given numbers is 13 x 1 x 178 = 2314
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/2314
Therefore, the GCF of Fractions 548/13,784/2314 is 4/2314
Least Common Multiple of 13,2314 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 13,2314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,2314) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(13,2314) x common factors =13 x 1 = 13
LCM(13,2314) = ( 13 × 2314 ) / 13
LCM(13,2314) = 30082 / 13
LCM(13,2314) = 2314
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FAQs on GCF of Fractions of 548/13, 784/2314
1. What is the HCF of 548,784?
The HCF of 548,784 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 548/13, 784/2314?
Answer: GCF of Numerators as per given numbers 548/13, 784/2314 is
GCF of Numerators i.e. for 548,784 is 4
LCM of denominators i.e. for 13,2314 is 2314.
Thus, GCF of Fractions is 4/2314.Finally, GCF of Fractions for 548/13, 784/2314 is 4/2314.