GCF of 825/12, 270/402
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 825/12, 270/402 i.e 15/804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 825/12, 270/402.
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 825/12,270/402?
Given fractions are 825/12,270/402
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 825/12,270/402, numerators are 825,270
Denominators are 12,402
The GCF of 825,270 is 15 .
LCM of 12,402 is 804.
The greatest common factor of 825/12,270/402 = [GCF of 825,270]/[LCM of 12,402]= 15/804
Therefore, the GCF of 825/12,270/402 is 15/804.
To find the highest common factor of 825,270, 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 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The HCF of 825,270 is 15.
Lets's calculate GCF of 825,270
| 3 | 825, 270 |
| 5 | 275, 90 |
| 55, 18 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 825,270 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 270
:1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270
Greatest Common Factor
We found the factors 825,270 . The biggest common factor number is the GCF number.
So the greatest common factor 825,270 is 15.
Lets's calculate LCM of 12,402
| 2 | 12, 402 |
| 3 | 6, 201 |
| 2, 67 |
∴ So the LCM of the given numbers is 2 x 3 x 2 x 67 = 804
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/804
Therefore, the GCF of Fractions 825/12,270/402 is 15/804
Least Common Multiple of 12,402 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 12,402 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,402) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(12,402) x common factors =6 x 1 = 6
LCM(12,402) = ( 12 × 402 ) / 6
LCM(12,402) = 4824 / 6
LCM(12,402) = 804
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FAQs on GCF of Fractions of 825/12, 270/402
1. What is the HCF of 825,270?
The HCF of 825,270 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 825/12, 270/402?
Answer: GCF of Numerators as per given numbers 825/12, 270/402 is
GCF of Numerators i.e. for 825,270 is 15
LCM of denominators i.e. for 12,402 is 804.
Thus, GCF of Fractions is 15/804.Finally, GCF of Fractions for 825/12, 270/402 is 15/804.