GCF of 825/23, 975/384
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 825/23, 975/384 i.e 75/8832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 825/23, 975/384.
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 825/23,975/384?
Given fractions are 825/23,975/384
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 825/23,975/384, numerators are 825,975
Denominators are 23,384
The GCF of 825,975 is 75 .
LCM of 23,384 is 8832.
The greatest common factor of 825/23,975/384 = [GCF of 825,975]/[LCM of 23,384]= 75/8832
Therefore, the GCF of 825/23,975/384 is 75/8832.
To find the highest common factor of 825,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 825,975 is 75.
Lets's calculate GCF of 825,975
| 3 | 825, 975 |
| 5 | 275, 325 |
| 5 | 55, 65 |
| 11, 13 |
∴ So the GCF of the given numbers is 3 x 5 x 5 = 75
Greatest Common Factor of 825,975 By Matching Biggest Common Factor Method
Now, list down the factors of 825
:1,3,5,11,15,25,33,55,75,165,275,825
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 825,975 . The biggest common factor number is the GCF number.
So the greatest common factor 825,975 is 75.
Lets's calculate LCM of 23,384
Given numbers has no common factors except 1. So, there LCM is their product i.e 8832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 75/8832
Therefore, the GCF of Fractions 825/23,975/384 is 75/8832
Least Common Multiple of 23,384 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 23,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(23,384) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(23,384) x common factors =1 x 1 = 1
LCM(23,384) = ( 23 × 384 ) / 1
LCM(23,384) = 8832 / 1
LCM(23,384) = 8832
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FAQs on GCF of Fractions of 825/23, 975/384
1. What is the HCF of 825,975?
The HCF of 825,975 is 75
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 825/23, 975/384?
Answer: GCF of Numerators as per given numbers 825/23, 975/384 is
GCF of Numerators i.e. for 825,975 is 75
LCM of denominators i.e. for 23,384 is 8832.
Thus, GCF of Fractions is 75/8832.Finally, GCF of Fractions for 825/23, 975/384 is 75/8832.