GCF of 2142/506, 2209/3404
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2142/506, 2209/3404 i.e 1/37444 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2142/506, 2209/3404.
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 2142/506,2209/3404?
Given fractions are 2142/506,2209/3404
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 2142/506,2209/3404, numerators are 2142,2209
Denominators are 506,3404
The GCF of 2142,2209 is 1 .
LCM of 506,3404 is 37444.
The greatest common factor of 2142/506,2209/3404 = [GCF of 2142,2209]/[LCM of 506,3404]= 1/37444
Therefore, the GCF of 2142/506,2209/3404 is 1/37444.
To find the highest common factor of 2142,2209, we have to find the factors of both numbers and list the highest common factor.
The factors of 2142 are 1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 306, 357, 714, 1071, 2142
The factors of 2209 are 1, 47, 2209
The HCF of 2142,2209 is 1.
Lets's calculate GCF of 2142,2209
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2142,2209 By Matching Biggest Common Factor Method
Now, list down the factors of 2142
:1,2,3,6,7,9,14,17,18,21,34,42,51,63,102,119,126,153,238,306,357,714,1071,2142
Now, list down the factors of 2209
:1,47,2209
Greatest Common Factor
We found the factors 2142,2209 . The biggest common factor number is the GCF number.
So the greatest common factor 2142,2209 is 1.
Lets's calculate LCM of 506,3404
| 2 | 506, 3404 |
| 23 | 253, 1702 |
| 11, 74 |
∴ So the LCM of the given numbers is 2 x 23 x 11 x 74 = 37444
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/37444
Therefore, the GCF of Fractions 2142/506,2209/3404 is 1/37444
Least Common Multiple of 506,3404 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 506,3404 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(506,3404) = 46
common factors(in case of two or more numbers have common factors) = 1
GCF(506,3404) x common factors =46 x 1 = 46
LCM(506,3404) = ( 506 × 3404 ) / 46
LCM(506,3404) = 1722424 / 46
LCM(506,3404) = 37444
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FAQs on GCF of Fractions of 2142/506, 2209/3404
1. What is the HCF of 2142,2209?
The HCF of 2142,2209 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 2142/506, 2209/3404?
Answer: GCF of Numerators as per given numbers 2142/506, 2209/3404 is
GCF of Numerators i.e. for 2142,2209 is 1
LCM of denominators i.e. for 506,3404 is 37444.
Thus, GCF of Fractions is 1/37444.Finally, GCF of Fractions for 2142/506, 2209/3404 is 1/37444.