GCF of 654/209, 2166/691
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 654/209, 2166/691 i.e 6/144419 easily. The following is the detailed procedure to determine the greatest common factor of fractions 654/209, 2166/691.
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 654/209,2166/691?
Given fractions are 654/209,2166/691
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 654/209,2166/691, numerators are 654,2166
Denominators are 209,691
The GCF of 654,2166 is 6 .
LCM of 209,691 is 144419.
The greatest common factor of 654/209,2166/691 = [GCF of 654,2166]/[LCM of 209,691]= 6/144419
Therefore, the GCF of 654/209,2166/691 is 6/144419.
To find the highest common factor of 654,2166, we have to find the factors of both numbers and list the highest common factor.
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The factors of 2166 are 1, 2, 3, 6, 19, 38, 57, 114, 361, 722, 1083, 2166
The HCF of 654,2166 is 6.
Lets's calculate GCF of 654,2166
| 2 | 654, 2166 |
| 3 | 327, 1083 |
| 109, 361 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 654,2166 By Matching Biggest Common Factor Method
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Now, list down the factors of 2166
:1,2,3,6,19,38,57,114,361,722,1083,2166
Greatest Common Factor
We found the factors 654,2166 . The biggest common factor number is the GCF number.
So the greatest common factor 654,2166 is 6.
Lets's calculate LCM of 209,691
Given numbers has no common factors except 1. So, there LCM is their product i.e 144419
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/144419
Therefore, the GCF of Fractions 654/209,2166/691 is 6/144419
Least Common Multiple of 209,691 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 209,691 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(209,691) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(209,691) x common factors =1 x 1 = 1
LCM(209,691) = ( 209 × 691 ) / 1
LCM(209,691) = 144419 / 1
LCM(209,691) = 144419
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FAQs on GCF of Fractions of 654/209, 2166/691
1. What is the HCF of 654,2166?
The HCF of 654,2166 is 6
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 654/209, 2166/691?
Answer: GCF of Numerators as per given numbers 654/209, 2166/691 is
GCF of Numerators i.e. for 654,2166 is 6
LCM of denominators i.e. for 209,691 is 144419.
Thus, GCF of Fractions is 6/144419.Finally, GCF of Fractions for 654/209, 2166/691 is 6/144419.