GCF of 105/456, 1665/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 105/456, 1665/728 i.e 15/41496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/456, 1665/728.
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 105/456,1665/728?
Given fractions are 105/456,1665/728
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 105/456,1665/728, numerators are 105,1665
Denominators are 456,728
The GCF of 105,1665 is 15 .
LCM of 456,728 is 41496.
The greatest common factor of 105/456,1665/728 = [GCF of 105,1665]/[LCM of 456,728]= 15/41496
Therefore, the GCF of 105/456,1665/728 is 15/41496.
To find the highest common factor of 105,1665, we have to find the factors of both numbers and list the highest common factor.
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 1665 are 1, 3, 5, 9, 15, 37, 45, 111, 185, 333, 555, 1665
The HCF of 105,1665 is 15.
Lets's calculate GCF of 105,1665
| 3 | 105, 1665 |
| 5 | 35, 555 |
| 7, 111 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 105,1665 By Matching Biggest Common Factor Method
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Now, list down the factors of 1665
:1,3,5,9,15,37,45,111,185,333,555,1665
Greatest Common Factor
We found the factors 105,1665 . The biggest common factor number is the GCF number.
So the greatest common factor 105,1665 is 15.
Lets's calculate LCM of 456,728
| 2 | 456, 728 |
| 2 | 228, 364 |
| 2 | 114, 182 |
| 57, 91 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 57 x 91 = 41496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/41496
Therefore, the GCF of Fractions 105/456,1665/728 is 15/41496
Least Common Multiple of 456,728 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 456,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(456,728) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(456,728) x common factors =8 x 1 = 8
LCM(456,728) = ( 456 × 728 ) / 8
LCM(456,728) = 331968 / 8
LCM(456,728) = 41496
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FAQs on GCF of Fractions of 105/456, 1665/728
1. What is the HCF of 105,1665?
The HCF of 105,1665 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 105/456, 1665/728?
Answer: GCF of Numerators as per given numbers 105/456, 1665/728 is
GCF of Numerators i.e. for 105,1665 is 15
LCM of denominators i.e. for 456,728 is 41496.
Thus, GCF of Fractions is 15/41496.Finally, GCF of Fractions for 105/456, 1665/728 is 15/41496.