GCF of 2108/452, 3870/2414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2108/452, 3870/2414 i.e 2/545564 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2108/452, 3870/2414.
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 2108/452,3870/2414?
Given fractions are 2108/452,3870/2414
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 2108/452,3870/2414, numerators are 2108,3870
Denominators are 452,2414
The GCF of 2108,3870 is 2 .
LCM of 452,2414 is 545564.
The greatest common factor of 2108/452,3870/2414 = [GCF of 2108,3870]/[LCM of 452,2414]= 2/545564
Therefore, the GCF of 2108/452,3870/2414 is 2/545564.
To find the highest common factor of 2108,3870, we have to find the factors of both numbers and list the highest common factor.
The factors of 2108 are 1, 2, 4, 17, 31, 34, 62, 68, 124, 527, 1054, 2108
The factors of 3870 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 43, 45, 86, 90, 129, 215, 258, 387, 430, 645, 774, 1290, 1935, 3870
The HCF of 2108,3870 is 2.
Lets's calculate GCF of 2108,3870
| 2 | 2108, 3870 |
| 1054, 1935 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2108,3870 By Matching Biggest Common Factor Method
Now, list down the factors of 2108
:1,2,4,17,31,34,62,68,124,527,1054,2108
Now, list down the factors of 3870
:1,2,3,5,6,9,10,15,18,30,43,45,86,90,129,215,258,387,430,645,774,1290,1935,3870
Greatest Common Factor
We found the factors 2108,3870 . The biggest common factor number is the GCF number.
So the greatest common factor 2108,3870 is 2.
Lets's calculate LCM of 452,2414
| 2 | 452, 2414 |
| 226, 1207 |
∴ So the LCM of the given numbers is 2 x 226 x 1207 = 545564
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/545564
Therefore, the GCF of Fractions 2108/452,3870/2414 is 2/545564
Least Common Multiple of 452,2414 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 452,2414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(452,2414) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(452,2414) x common factors =2 x 1 = 2
LCM(452,2414) = ( 452 × 2414 ) / 2
LCM(452,2414) = 1091128 / 2
LCM(452,2414) = 545564
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FAQs on GCF of Fractions of 2108/452, 3870/2414
1. What is the HCF of 2108,3870?
The HCF of 2108,3870 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 2108/452, 3870/2414?
Answer: GCF of Numerators as per given numbers 2108/452, 3870/2414 is
GCF of Numerators i.e. for 2108,3870 is 2
LCM of denominators i.e. for 452,2414 is 545564.
Thus, GCF of Fractions is 2/545564.Finally, GCF of Fractions for 2108/452, 3870/2414 is 2/545564.