GCF of 1826/312, 3564/5413
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1826/312, 3564/5413 i.e 22/1688856 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1826/312, 3564/5413.
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 1826/312,3564/5413?
Given fractions are 1826/312,3564/5413
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 1826/312,3564/5413, numerators are 1826,3564
Denominators are 312,5413
The GCF of 1826,3564 is 22 .
LCM of 312,5413 is 1688856.
The greatest common factor of 1826/312,3564/5413 = [GCF of 1826,3564]/[LCM of 312,5413]= 22/1688856
Therefore, the GCF of 1826/312,3564/5413 is 22/1688856.
To find the highest common factor of 1826,3564, we have to find the factors of both numbers and list the highest common factor.
The factors of 1826 are 1, 2, 11, 22, 83, 166, 913, 1826
The factors of 3564 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 81, 99, 108, 132, 162, 198, 297, 324, 396, 594, 891, 1188, 1782, 3564
The HCF of 1826,3564 is 22.
Lets's calculate GCF of 1826,3564
| 2 | 1826, 3564 |
| 11 | 913, 1782 |
| 83, 162 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 1826,3564 By Matching Biggest Common Factor Method
Now, list down the factors of 1826
:1,2,11,22,83,166,913,1826
Now, list down the factors of 3564
:1,2,3,4,6,9,11,12,18,22,27,33,36,44,54,66,81,99,108,132,162,198,297,324,396,594,891,1188,1782,3564
Greatest Common Factor
We found the factors 1826,3564 . The biggest common factor number is the GCF number.
So the greatest common factor 1826,3564 is 22.
Lets's calculate LCM of 312,5413
Given numbers has no common factors except 1. So, there LCM is their product i.e 1688856
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/1688856
Therefore, the GCF of Fractions 1826/312,3564/5413 is 22/1688856
Least Common Multiple of 312,5413 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 312,5413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,5413) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(312,5413) x common factors =1 x 1 = 1
LCM(312,5413) = ( 312 × 5413 ) / 1
LCM(312,5413) = 1688856 / 1
LCM(312,5413) = 1688856
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FAQs on GCF of Fractions of 1826/312, 3564/5413
1. What is the HCF of 1826,3564?
The HCF of 1826,3564 is 22
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 1826/312, 3564/5413?
Answer: GCF of Numerators as per given numbers 1826/312, 3564/5413 is
GCF of Numerators i.e. for 1826,3564 is 22
LCM of denominators i.e. for 312,5413 is 1688856.
Thus, GCF of Fractions is 22/1688856.Finally, GCF of Fractions for 1826/312, 3564/5413 is 22/1688856.