GCF of 1805/742, 2109/454
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1805/742, 2109/454 i.e 19/168434 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1805/742, 2109/454.
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 1805/742,2109/454?
Given fractions are 1805/742,2109/454
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 1805/742,2109/454, numerators are 1805,2109
Denominators are 742,454
The GCF of 1805,2109 is 19 .
LCM of 742,454 is 168434.
The greatest common factor of 1805/742,2109/454 = [GCF of 1805,2109]/[LCM of 742,454]= 19/168434
Therefore, the GCF of 1805/742,2109/454 is 19/168434.
To find the highest common factor of 1805,2109, we have to find the factors of both numbers and list the highest common factor.
The factors of 1805 are 1, 5, 19, 95, 361, 1805
The factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109
The HCF of 1805,2109 is 19.
Lets's calculate GCF of 1805,2109
| 19 | 1805, 2109 |
| 95, 111 |
∴ So the GCF of the given numbers is 19 = 19
Greatest Common Factor of 1805,2109 By Matching Biggest Common Factor Method
Now, list down the factors of 1805
:1,5,19,95,361,1805
Now, list down the factors of 2109
:1,3,19,37,57,111,703,2109
Greatest Common Factor
We found the factors 1805,2109 . The biggest common factor number is the GCF number.
So the greatest common factor 1805,2109 is 19.
Lets's calculate LCM of 742,454
| 2 | 742, 454 |
| 371, 227 |
∴ So the LCM of the given numbers is 2 x 371 x 227 = 168434
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/168434
Therefore, the GCF of Fractions 1805/742,2109/454 is 19/168434
Least Common Multiple of 742,454 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 742,454 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(742,454) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(742,454) x common factors =2 x 1 = 2
LCM(742,454) = ( 742 × 454 ) / 2
LCM(742,454) = 336868 / 2
LCM(742,454) = 168434
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FAQs on GCF of Fractions of 1805/742, 2109/454
1. What is the HCF of 1805,2109?
The HCF of 1805,2109 is 19
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 1805/742, 2109/454?
Answer: GCF of Numerators as per given numbers 1805/742, 2109/454 is
GCF of Numerators i.e. for 1805,2109 is 19
LCM of denominators i.e. for 742,454 is 168434.
Thus, GCF of Fractions is 19/168434.Finally, GCF of Fractions for 1805/742, 2109/454 is 19/168434.