GCF of 825/623, 828/712
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 825/623, 828/712 i.e 3/4984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 825/623, 828/712.
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 825/623,828/712?
Given fractions are 825/623,828/712
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 825/623,828/712, numerators are 825,828
Denominators are 623,712
The GCF of 825,828 is 3 .
LCM of 623,712 is 4984.
The greatest common factor of 825/623,828/712 = [GCF of 825,828]/[LCM of 623,712]= 3/4984
Therefore, the GCF of 825/623,828/712 is 3/4984.
To find the highest common factor of 825,828, 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 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The HCF of 825,828 is 3.
Lets's calculate GCF of 825,828
| 3 | 825, 828 |
| 275, 276 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 825,828 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 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Greatest Common Factor
We found the factors 825,828 . The biggest common factor number is the GCF number.
So the greatest common factor 825,828 is 3.
Lets's calculate LCM of 623,712
| 89 | 623, 712 |
| 7, 8 |
∴ So the LCM of the given numbers is 89 x 7 x 8 = 4984
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/4984
Therefore, the GCF of Fractions 825/623,828/712 is 3/4984
Least Common Multiple of 623,712 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 623,712 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(623,712) = 89
common factors(in case of two or more numbers have common factors) = 1
GCF(623,712) x common factors =89 x 1 = 89
LCM(623,712) = ( 623 × 712 ) / 89
LCM(623,712) = 443576 / 89
LCM(623,712) = 4984
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FAQs on GCF of Fractions of 825/623, 828/712
1. What is the HCF of 825,828?
The HCF of 825,828 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 825/623, 828/712?
Answer: GCF of Numerators as per given numbers 825/623, 828/712 is
GCF of Numerators i.e. for 825,828 is 3
LCM of denominators i.e. for 623,712 is 4984.
Thus, GCF of Fractions is 3/4984.Finally, GCF of Fractions for 825/623, 828/712 is 3/4984.