GCF of 309/30, 420/118
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 309/30, 420/118 i.e 3/1770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 309/30, 420/118.
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 309/30,420/118?
Given fractions are 309/30,420/118
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 309/30,420/118, numerators are 309,420
Denominators are 30,118
The GCF of 309,420 is 3 .
LCM of 30,118 is 1770.
The greatest common factor of 309/30,420/118 = [GCF of 309,420]/[LCM of 30,118]= 3/1770
Therefore, the GCF of 309/30,420/118 is 3/1770.
To find the highest common factor of 309,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 309 are 1, 3, 103, 309
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 309,420 is 3.
Lets's calculate GCF of 309,420
| 3 | 309, 420 |
| 103, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 309,420 By Matching Biggest Common Factor Method
Now, list down the factors of 309
:1,3,103,309
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 309,420 . The biggest common factor number is the GCF number.
So the greatest common factor 309,420 is 3.
Lets's calculate LCM of 30,118
| 2 | 30, 118 |
| 15, 59 |
∴ So the LCM of the given numbers is 2 x 15 x 59 = 1770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1770
Therefore, the GCF of Fractions 309/30,420/118 is 3/1770
Least Common Multiple of 30,118 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 30,118 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,118) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(30,118) x common factors =2 x 1 = 2
LCM(30,118) = ( 30 × 118 ) / 2
LCM(30,118) = 3540 / 2
LCM(30,118) = 1770
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FAQs on GCF of Fractions of 309/30, 420/118
1. What is the HCF of 309,420?
The HCF of 309,420 is 3
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 309/30, 420/118?
Answer: GCF of Numerators as per given numbers 309/30, 420/118 is
GCF of Numerators i.e. for 309,420 is 3
LCM of denominators i.e. for 30,118 is 1770.
Thus, GCF of Fractions is 3/1770.Finally, GCF of Fractions for 309/30, 420/118 is 3/1770.