GCF of 3120/309, 2642/729
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3120/309, 2642/729 i.e 2/75087 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3120/309, 2642/729.
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 3120/309,2642/729?
Given fractions are 3120/309,2642/729
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 3120/309,2642/729, numerators are 3120,2642
Denominators are 309,729
The GCF of 3120,2642 is 2 .
LCM of 309,729 is 75087.
The greatest common factor of 3120/309,2642/729 = [GCF of 3120,2642]/[LCM of 309,729]= 2/75087
Therefore, the GCF of 3120/309,2642/729 is 2/75087.
To find the highest common factor of 3120,2642, we have to find the factors of both numbers and list the highest common factor.
The factors of 3120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 39, 40, 48, 52, 60, 65, 78, 80, 104, 120, 130, 156, 195, 208, 240, 260, 312, 390, 520, 624, 780, 1040, 1560, 3120
The factors of 2642 are 1, 2, 1321, 2642
The HCF of 3120,2642 is 2.
Lets's calculate GCF of 3120,2642
| 2 | 3120, 2642 |
| 1560, 1321 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 3120,2642 By Matching Biggest Common Factor Method
Now, list down the factors of 3120
:1,2,3,4,5,6,8,10,12,13,15,16,20,24,26,30,39,40,48,52,60,65,78,80,104,120,130,156,195,208,240,260,312,390,520,624,780,1040,1560,3120
Now, list down the factors of 2642
:1,2,1321,2642
Greatest Common Factor
We found the factors 3120,2642 . The biggest common factor number is the GCF number.
So the greatest common factor 3120,2642 is 2.
Lets's calculate LCM of 309,729
| 3 | 309, 729 |
| 103, 243 |
∴ So the LCM of the given numbers is 3 x 103 x 243 = 75087
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/75087
Therefore, the GCF of Fractions 3120/309,2642/729 is 2/75087
Least Common Multiple of 309,729 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 309,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,729) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,729) x common factors =3 x 1 = 3
LCM(309,729) = ( 309 × 729 ) / 3
LCM(309,729) = 225261 / 3
LCM(309,729) = 75087
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FAQs on GCF of Fractions of 3120/309, 2642/729
1. What is the HCF of 3120,2642?
The HCF of 3120,2642 is 2
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 3120/309, 2642/729?
Answer: GCF of Numerators as per given numbers 3120/309, 2642/729 is
GCF of Numerators i.e. for 3120,2642 is 2
LCM of denominators i.e. for 309,729 is 75087.
Thus, GCF of Fractions is 2/75087.Finally, GCF of Fractions for 3120/309, 2642/729 is 2/75087.