GCF of 3414/352, 9075/825
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3414/352, 9075/825 i.e 3/26400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3414/352, 9075/825.
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 3414/352,9075/825?
Given fractions are 3414/352,9075/825
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 3414/352,9075/825, numerators are 3414,9075
Denominators are 352,825
The GCF of 3414,9075 is 3 .
LCM of 352,825 is 26400.
The greatest common factor of 3414/352,9075/825 = [GCF of 3414,9075]/[LCM of 352,825]= 3/26400
Therefore, the GCF of 3414/352,9075/825 is 3/26400.
To find the highest common factor of 3414,9075, we have to find the factors of both numbers and list the highest common factor.
The factors of 3414 are 1, 2, 3, 6, 569, 1138, 1707, 3414
The factors of 9075 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 121, 165, 275, 363, 605, 825, 1815, 3025, 9075
The HCF of 3414,9075 is 3.
Lets's calculate GCF of 3414,9075
| 3 | 3414, 9075 |
| 1138, 3025 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3414,9075 By Matching Biggest Common Factor Method
Now, list down the factors of 3414
:1,2,3,6,569,1138,1707,3414
Now, list down the factors of 9075
:1,3,5,11,15,25,33,55,75,121,165,275,363,605,825,1815,3025,9075
Greatest Common Factor
We found the factors 3414,9075 . The biggest common factor number is the GCF number.
So the greatest common factor 3414,9075 is 3.
Lets's calculate LCM of 352,825
| 11 | 352, 825 |
| 32, 75 |
∴ So the LCM of the given numbers is 11 x 32 x 75 = 26400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/26400
Therefore, the GCF of Fractions 3414/352,9075/825 is 3/26400
Least Common Multiple of 352,825 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 352,825 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(352,825) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(352,825) x common factors =11 x 1 = 11
LCM(352,825) = ( 352 × 825 ) / 11
LCM(352,825) = 290400 / 11
LCM(352,825) = 26400
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FAQs on GCF of Fractions of 3414/352, 9075/825
1. What is the HCF of 3414,9075?
The HCF of 3414,9075 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 3414/352, 9075/825?
Answer: GCF of Numerators as per given numbers 3414/352, 9075/825 is
GCF of Numerators i.e. for 3414,9075 is 3
LCM of denominators i.e. for 352,825 is 26400.
Thus, GCF of Fractions is 3/26400.Finally, GCF of Fractions for 3414/352, 9075/825 is 3/26400.