GCF of 6/20, 40/22, 39/103, 654/309
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6/20, 40/22, 39/103, 654/309 i.e 1/67980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6/20, 40/22, 39/103, 654/309.
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 6/20,40/22,39/103,654/309?
Given fractions are 6/20,40/22,39/103,654/309
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 6/20,40/22,39/103,654/309, numerators are 6,40,39,654
Denominators are 20,22,103,309
The GCF of 6,40,39,654 is 1 .
LCM of 20,22,103,309 is 67980.
The greatest common factor of 6/20,40/22,39/103,654/309 = [GCF of 6,40,39,654]/[LCM of 20,22,103,309]= 1/67980
Therefore, the GCF of 6/20,40/22,39/103,654/309 is 1/67980.
To find the highest common factor of 6,40,39,654, we have to find the factors of both numbers and list the highest common factor.
The factors of 6 are 1, 2, 3, 6
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 39 are 1, 3, 13, 39
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 6,40,39,654 is 1.
Lets's calculate GCF of 6,40,39,654
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6,40,39,654 By Matching Biggest Common Factor Method
Now, list down the factors of 6
:1,2,3,6
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 39
:1,3,13,39
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 6,40,39,654 . The biggest common factor number is the GCF number.
So the greatest common factor 6,40,39,654 is 1.
Lets's calculate LCM of 20,22,103,309
| 2 | 20, 22, 103, 309 |
| 103 | 10, 11, 103, 309 |
| 10, 11, 1, 3 |
∴ So the LCM of the given numbers is 2 x 103 x 10 x 11 x 1 x 3 = 67980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/67980
Therefore, the GCF of Fractions 6/20,40/22,39/103,654/309 is 1/67980
Least Common Multiple of 20,22,103,309 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 20,22,103,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,22,103,309) = 1
common factors(in case of two or more numbers have common factors) = 206
GCF(20,22,103,309) x common factors =1 x 206 = 206
LCM(20,22,103,309) = ( 20 × 22 × 103 × 309 ) / 206
LCM(20,22,103,309) = 14003880 / 206
LCM(20,22,103,309) = 67980
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 6/20, 40/22, 39/103, 654/309
1. What is the HCF of 6,40,39,654?
The HCF of 6,40,39,654 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 6/20, 40/22, 39/103, 654/309?
Answer: GCF of Numerators as per given numbers 6/20, 40/22, 39/103, 654/309 is
GCF of Numerators i.e. for 6,40,39,654 is 1
LCM of denominators i.e. for 20,22,103,309 is 67980.
Thus, GCF of Fractions is 1/67980.Finally, GCF of Fractions for 6/20, 40/22, 39/103, 654/309 is 1/67980.