GCF of 783/14, 825/1632
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 783/14, 825/1632 i.e 3/11424 easily. The following is the detailed procedure to determine the greatest common factor of fractions 783/14, 825/1632.
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 783/14,825/1632?
Given fractions are 783/14,825/1632
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 783/14,825/1632, numerators are 783,825
Denominators are 14,1632
The GCF of 783,825 is 3 .
LCM of 14,1632 is 11424.
The greatest common factor of 783/14,825/1632 = [GCF of 783,825]/[LCM of 14,1632]= 3/11424
Therefore, the GCF of 783/14,825/1632 is 3/11424.
To find the highest common factor of 783,825, we have to find the factors of both numbers and list the highest common factor.
The factors of 783 are 1, 3, 9, 27, 29, 87, 261, 783
The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
The HCF of 783,825 is 3.
Lets's calculate GCF of 783,825
| 3 | 783, 825 |
| 261, 275 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 783,825 By Matching Biggest Common Factor Method
Now, list down the factors of 783
:1,3,9,27,29,87,261,783
Now, list down the factors of 825
:1,3,5,11,15,25,33,55,75,165,275,825
Greatest Common Factor
We found the factors 783,825 . The biggest common factor number is the GCF number.
So the greatest common factor 783,825 is 3.
Lets's calculate LCM of 14,1632
| 2 | 14, 1632 |
| 7, 816 |
∴ So the LCM of the given numbers is 2 x 7 x 816 = 11424
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/11424
Therefore, the GCF of Fractions 783/14,825/1632 is 3/11424
Least Common Multiple of 14,1632 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 14,1632 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,1632) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(14,1632) x common factors =2 x 1 = 2
LCM(14,1632) = ( 14 × 1632 ) / 2
LCM(14,1632) = 22848 / 2
LCM(14,1632) = 11424
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FAQs on GCF of Fractions of 783/14, 825/1632
1. What is the HCF of 783,825?
The HCF of 783,825 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 783/14, 825/1632?
Answer: GCF of Numerators as per given numbers 783/14, 825/1632 is
GCF of Numerators i.e. for 783,825 is 3
LCM of denominators i.e. for 14,1632 is 11424.
Thus, GCF of Fractions is 3/11424.Finally, GCF of Fractions for 783/14, 825/1632 is 3/11424.