GCF of 3825/414, 1971/804
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3825/414, 1971/804 i.e 9/55476 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3825/414, 1971/804.
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 3825/414,1971/804?
Given fractions are 3825/414,1971/804
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 3825/414,1971/804, numerators are 3825,1971
Denominators are 414,804
The GCF of 3825,1971 is 9 .
LCM of 414,804 is 55476.
The greatest common factor of 3825/414,1971/804 = [GCF of 3825,1971]/[LCM of 414,804]= 9/55476
Therefore, the GCF of 3825/414,1971/804 is 9/55476.
To find the highest common factor of 3825,1971, we have to find the factors of both numbers and list the highest common factor.
The factors of 3825 are 1, 3, 5, 9, 15, 17, 25, 45, 51, 75, 85, 153, 225, 255, 425, 765, 1275, 3825
The factors of 1971 are 1, 3, 9, 27, 73, 219, 657, 1971
The HCF of 3825,1971 is 9.
Lets's calculate GCF of 3825,1971
| 3 | 3825, 1971 |
| 3 | 1275, 657 |
| 425, 219 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 3825,1971 By Matching Biggest Common Factor Method
Now, list down the factors of 3825
:1,3,5,9,15,17,25,45,51,75,85,153,225,255,425,765,1275,3825
Now, list down the factors of 1971
:1,3,9,27,73,219,657,1971
Greatest Common Factor
We found the factors 3825,1971 . The biggest common factor number is the GCF number.
So the greatest common factor 3825,1971 is 9.
Lets's calculate LCM of 414,804
| 2 | 414, 804 |
| 3 | 207, 402 |
| 69, 134 |
∴ So the LCM of the given numbers is 2 x 3 x 69 x 134 = 55476
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/55476
Therefore, the GCF of Fractions 3825/414,1971/804 is 9/55476
Least Common Multiple of 414,804 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 414,804 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,804) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(414,804) x common factors =6 x 1 = 6
LCM(414,804) = ( 414 × 804 ) / 6
LCM(414,804) = 332856 / 6
LCM(414,804) = 55476
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FAQs on GCF of Fractions of 3825/414, 1971/804
1. What is the HCF of 3825,1971?
The HCF of 3825,1971 is 9
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 3825/414, 1971/804?
Answer: GCF of Numerators as per given numbers 3825/414, 1971/804 is
GCF of Numerators i.e. for 3825,1971 is 9
LCM of denominators i.e. for 414,804 is 55476.
Thus, GCF of Fractions is 9/55476.Finally, GCF of Fractions for 3825/414, 1971/804 is 9/55476.