GCF of 612/384, 825/430
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 612/384, 825/430 i.e 3/82560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 612/384, 825/430.
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 612/384,825/430?
Given fractions are 612/384,825/430
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 612/384,825/430, numerators are 612,825
Denominators are 384,430
The GCF of 612,825 is 3 .
LCM of 384,430 is 82560.
The greatest common factor of 612/384,825/430 = [GCF of 612,825]/[LCM of 384,430]= 3/82560
Therefore, the GCF of 612/384,825/430 is 3/82560.
To find the highest common factor of 612,825, we have to find the factors of both numbers and list the highest common factor.
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
The HCF of 612,825 is 3.
Lets's calculate GCF of 612,825
| 3 | 612, 825 |
| 204, 275 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 612,825 By Matching Biggest Common Factor Method
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Now, list down the factors of 825
:1,3,5,11,15,25,33,55,75,165,275,825
Greatest Common Factor
We found the factors 612,825 . The biggest common factor number is the GCF number.
So the greatest common factor 612,825 is 3.
Lets's calculate LCM of 384,430
| 2 | 384, 430 |
| 192, 215 |
∴ So the LCM of the given numbers is 2 x 192 x 215 = 82560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/82560
Therefore, the GCF of Fractions 612/384,825/430 is 3/82560
Least Common Multiple of 384,430 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 384,430 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(384,430) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(384,430) x common factors =2 x 1 = 2
LCM(384,430) = ( 384 × 430 ) / 2
LCM(384,430) = 165120 / 2
LCM(384,430) = 82560
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FAQs on GCF of Fractions of 612/384, 825/430
1. What is the HCF of 612,825?
The HCF of 612,825 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 612/384, 825/430?
Answer: GCF of Numerators as per given numbers 612/384, 825/430 is
GCF of Numerators i.e. for 612,825 is 3
LCM of denominators i.e. for 384,430 is 82560.
Thus, GCF of Fractions is 3/82560.Finally, GCF of Fractions for 612/384, 825/430 is 3/82560.