GCF of 1725/864, 3870/6324
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1725/864, 3870/6324 i.e 15/455328 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1725/864, 3870/6324.
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 1725/864,3870/6324?
Given fractions are 1725/864,3870/6324
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 1725/864,3870/6324, numerators are 1725,3870
Denominators are 864,6324
The GCF of 1725,3870 is 15 .
LCM of 864,6324 is 455328.
The greatest common factor of 1725/864,3870/6324 = [GCF of 1725,3870]/[LCM of 864,6324]= 15/455328
Therefore, the GCF of 1725/864,3870/6324 is 15/455328.
To find the highest common factor of 1725,3870, we have to find the factors of both numbers and list the highest common factor.
The factors of 1725 are 1, 3, 5, 15, 23, 25, 69, 75, 115, 345, 575, 1725
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 1725,3870 is 15.
Lets's calculate GCF of 1725,3870
| 3 | 1725, 3870 |
| 5 | 575, 1290 |
| 115, 258 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 1725,3870 By Matching Biggest Common Factor Method
Now, list down the factors of 1725
:1,3,5,15,23,25,69,75,115,345,575,1725
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 1725,3870 . The biggest common factor number is the GCF number.
So the greatest common factor 1725,3870 is 15.
Lets's calculate LCM of 864,6324
| 2 | 864, 6324 |
| 2 | 432, 3162 |
| 3 | 216, 1581 |
| 72, 527 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 72 x 527 = 455328
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/455328
Therefore, the GCF of Fractions 1725/864,3870/6324 is 15/455328
Least Common Multiple of 864,6324 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 864,6324 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(864,6324) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(864,6324) x common factors =12 x 1 = 12
LCM(864,6324) = ( 864 × 6324 ) / 12
LCM(864,6324) = 5463936 / 12
LCM(864,6324) = 455328
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FAQs on GCF of Fractions of 1725/864, 3870/6324
1. What is the HCF of 1725,3870?
The HCF of 1725,3870 is 15
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 1725/864, 3870/6324?
Answer: GCF of Numerators as per given numbers 1725/864, 3870/6324 is
GCF of Numerators i.e. for 1725,3870 is 15
LCM of denominators i.e. for 864,6324 is 455328.
Thus, GCF of Fractions is 15/455328.Finally, GCF of Fractions for 1725/864, 3870/6324 is 15/455328.