GCF of 1860/305, 2232/1421
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1860/305, 2232/1421 i.e 372/433405 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1860/305, 2232/1421.
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 1860/305,2232/1421?
Given fractions are 1860/305,2232/1421
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 1860/305,2232/1421, numerators are 1860,2232
Denominators are 305,1421
The GCF of 1860,2232 is 372 .
LCM of 305,1421 is 433405.
The greatest common factor of 1860/305,2232/1421 = [GCF of 1860,2232]/[LCM of 305,1421]= 372/433405
Therefore, the GCF of 1860/305,2232/1421 is 372/433405.
To find the highest common factor of 1860,2232, we have to find the factors of both numbers and list the highest common factor.
The factors of 1860 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 31, 60, 62, 93, 124, 155, 186, 310, 372, 465, 620, 930, 1860
The factors of 2232 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 31, 36, 62, 72, 93, 124, 186, 248, 279, 372, 558, 744, 1116, 2232
The HCF of 1860,2232 is 372.
Lets's calculate GCF of 1860,2232
| 2 | 1860, 2232 |
| 2 | 930, 1116 |
| 3 | 465, 558 |
| 31 | 155, 186 |
| 5, 6 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 31 = 372
Greatest Common Factor of 1860,2232 By Matching Biggest Common Factor Method
Now, list down the factors of 1860
:1,2,3,4,5,6,10,12,15,20,30,31,60,62,93,124,155,186,310,372,465,620,930,1860
Now, list down the factors of 2232
:1,2,3,4,6,8,9,12,18,24,31,36,62,72,93,124,186,248,279,372,558,744,1116,2232
Greatest Common Factor
We found the factors 1860,2232 . The biggest common factor number is the GCF number.
So the greatest common factor 1860,2232 is 372.
Lets's calculate LCM of 305,1421
Given numbers has no common factors except 1. So, there LCM is their product i.e 433405
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 372/433405
Therefore, the GCF of Fractions 1860/305,2232/1421 is 372/433405
Least Common Multiple of 305,1421 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 305,1421 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(305,1421) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(305,1421) x common factors =1 x 1 = 1
LCM(305,1421) = ( 305 × 1421 ) / 1
LCM(305,1421) = 433405 / 1
LCM(305,1421) = 433405
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FAQs on GCF of Fractions of 1860/305, 2232/1421
1. What is the HCF of 1860,2232?
The HCF of 1860,2232 is 372
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 1860/305, 2232/1421?
Answer: GCF of Numerators as per given numbers 1860/305, 2232/1421 is
GCF of Numerators i.e. for 1860,2232 is 372
LCM of denominators i.e. for 305,1421 is 433405.
Thus, GCF of Fractions is 372/433405.Finally, GCF of Fractions for 1860/305, 2232/1421 is 372/433405.