GCF of 2049/528, 2085/7648
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2049/528, 2085/7648 i.e 3/252384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2049/528, 2085/7648.
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 2049/528,2085/7648?
Given fractions are 2049/528,2085/7648
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 2049/528,2085/7648, numerators are 2049,2085
Denominators are 528,7648
The GCF of 2049,2085 is 3 .
LCM of 528,7648 is 252384.
The greatest common factor of 2049/528,2085/7648 = [GCF of 2049,2085]/[LCM of 528,7648]= 3/252384
Therefore, the GCF of 2049/528,2085/7648 is 3/252384.
To find the highest common factor of 2049,2085, we have to find the factors of both numbers and list the highest common factor.
The factors of 2049 are 1, 3, 683, 2049
The factors of 2085 are 1, 3, 5, 15, 139, 417, 695, 2085
The HCF of 2049,2085 is 3.
Lets's calculate GCF of 2049,2085
| 3 | 2049, 2085 |
| 683, 695 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2049,2085 By Matching Biggest Common Factor Method
Now, list down the factors of 2049
:1,3,683,2049
Now, list down the factors of 2085
:1,3,5,15,139,417,695,2085
Greatest Common Factor
We found the factors 2049,2085 . The biggest common factor number is the GCF number.
So the greatest common factor 2049,2085 is 3.
Lets's calculate LCM of 528,7648
| 2 | 528, 7648 |
| 2 | 264, 3824 |
| 2 | 132, 1912 |
| 2 | 66, 956 |
| 33, 478 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 33 x 478 = 252384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/252384
Therefore, the GCF of Fractions 2049/528,2085/7648 is 3/252384
Least Common Multiple of 528,7648 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 528,7648 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(528,7648) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(528,7648) x common factors =16 x 1 = 16
LCM(528,7648) = ( 528 × 7648 ) / 16
LCM(528,7648) = 4038144 / 16
LCM(528,7648) = 252384
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FAQs on GCF of Fractions of 2049/528, 2085/7648
1. What is the HCF of 2049,2085?
The HCF of 2049,2085 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 2049/528, 2085/7648?
Answer: GCF of Numerators as per given numbers 2049/528, 2085/7648 is
GCF of Numerators i.e. for 2049,2085 is 3
LCM of denominators i.e. for 528,7648 is 252384.
Thus, GCF of Fractions is 3/252384.Finally, GCF of Fractions for 2049/528, 2085/7648 is 3/252384.