GCF of 2310/360, 1408/238
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2310/360, 1408/238 i.e 22/42840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2310/360, 1408/238.
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 2310/360,1408/238?
Given fractions are 2310/360,1408/238
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 2310/360,1408/238, numerators are 2310,1408
Denominators are 360,238
The GCF of 2310,1408 is 22 .
LCM of 360,238 is 42840.
The greatest common factor of 2310/360,1408/238 = [GCF of 2310,1408]/[LCM of 360,238]= 22/42840
Therefore, the GCF of 2310/360,1408/238 is 22/42840.
To find the highest common factor of 2310,1408, we have to find the factors of both numbers and list the highest common factor.
The factors of 2310 are 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310
The factors of 1408 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704, 1408
The HCF of 2310,1408 is 22.
Lets's calculate GCF of 2310,1408
| 2 | 2310, 1408 |
| 11 | 1155, 704 |
| 105, 64 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 2310,1408 By Matching Biggest Common Factor Method
Now, list down the factors of 2310
:1,2,3,5,6,7,10,11,14,15,21,22,30,33,35,42,55,66,70,77,105,110,154,165,210,231,330,385,462,770,1155,2310
Now, list down the factors of 1408
:1,2,4,8,11,16,22,32,44,64,88,128,176,352,704,1408
Greatest Common Factor
We found the factors 2310,1408 . The biggest common factor number is the GCF number.
So the greatest common factor 2310,1408 is 22.
Lets's calculate LCM of 360,238
| 2 | 360, 238 |
| 180, 119 |
∴ So the LCM of the given numbers is 2 x 180 x 119 = 42840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/42840
Therefore, the GCF of Fractions 2310/360,1408/238 is 22/42840
Least Common Multiple of 360,238 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 360,238 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(360,238) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(360,238) x common factors =2 x 1 = 2
LCM(360,238) = ( 360 × 238 ) / 2
LCM(360,238) = 85680 / 2
LCM(360,238) = 42840
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FAQs on GCF of Fractions of 2310/360, 1408/238
1. What is the HCF of 2310,1408?
The HCF of 2310,1408 is 22
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 2310/360, 1408/238?
Answer: GCF of Numerators as per given numbers 2310/360, 1408/238 is
GCF of Numerators i.e. for 2310,1408 is 22
LCM of denominators i.e. for 360,238 is 42840.
Thus, GCF of Fractions is 22/42840.Finally, GCF of Fractions for 2310/360, 1408/238 is 22/42840.