GCF of 291/209, 420/148
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 291/209, 420/148 i.e 3/30932 easily. The following is the detailed procedure to determine the greatest common factor of fractions 291/209, 420/148.
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 291/209,420/148?
Given fractions are 291/209,420/148
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 291/209,420/148, numerators are 291,420
Denominators are 209,148
The GCF of 291,420 is 3 .
LCM of 209,148 is 30932.
The greatest common factor of 291/209,420/148 = [GCF of 291,420]/[LCM of 209,148]= 3/30932
Therefore, the GCF of 291/209,420/148 is 3/30932.
To find the highest common factor of 291,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 291 are 1, 3, 97, 291
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 291,420 is 3.
Lets's calculate GCF of 291,420
| 3 | 291, 420 |
| 97, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 291,420 By Matching Biggest Common Factor Method
Now, list down the factors of 291
:1,3,97,291
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 291,420 . The biggest common factor number is the GCF number.
So the greatest common factor 291,420 is 3.
Lets's calculate LCM of 209,148
Given numbers has no common factors except 1. So, there LCM is their product i.e 30932
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/30932
Therefore, the GCF of Fractions 291/209,420/148 is 3/30932
Least Common Multiple of 209,148 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 209,148 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(209,148) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(209,148) x common factors =1 x 1 = 1
LCM(209,148) = ( 209 × 148 ) / 1
LCM(209,148) = 30932 / 1
LCM(209,148) = 30932
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FAQs on GCF of Fractions of 291/209, 420/148
1. What is the HCF of 291,420?
The HCF of 291,420 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 291/209, 420/148?
Answer: GCF of Numerators as per given numbers 291/209, 420/148 is
GCF of Numerators i.e. for 291,420 is 3
LCM of denominators i.e. for 209,148 is 30932.
Thus, GCF of Fractions is 3/30932.Finally, GCF of Fractions for 291/209, 420/148 is 3/30932.