GCF of 353/48, 648/14, 289/40
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 353/48, 648/14, 289/40 i.e 1/1680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 353/48, 648/14, 289/40.
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 353/48,648/14,289/40?
Given fractions are 353/48,648/14,289/40
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 353/48,648/14,289/40, numerators are 353,648,289
Denominators are 48,14,40
The GCF of 353,648,289 is 1 .
LCM of 48,14,40 is 1680.
The greatest common factor of 353/48,648/14,289/40 = [GCF of 353,648,289]/[LCM of 48,14,40]= 1/1680
Therefore, the GCF of 353/48,648/14,289/40 is 1/1680.
To find the highest common factor of 353,648,289, we have to find the factors of both numbers and list the highest common factor.
The factors of 353 are 1, 353
The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
The factors of 289 are 1, 17, 289
The HCF of 353,648,289 is 1.
Lets's calculate GCF of 353,648,289
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 353,648,289 By Matching Biggest Common Factor Method
Now, list down the factors of 353
:1,353
Now, list down the factors of 648
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,324,648
Now, list down the factors of 289
:1,17,289
Greatest Common Factor
We found the factors 353,648,289 . The biggest common factor number is the GCF number.
So the greatest common factor 353,648,289 is 1.
Lets's calculate LCM of 48,14,40
| 2 | 48, 14, 40 |
| 2 | 24, 7, 20 |
| 2 | 12, 7, 10 |
| 6, 7, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 6 x 7 x 5 = 1680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1680
Therefore, the GCF of Fractions 353/48,648/14,289/40 is 1/1680
Least Common Multiple of 48,14,40 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 48,14,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,14,40) = 2
common factors(in case of two or more numbers have common factors) = 8
GCF(48,14,40) x common factors =2 x 8 = 16
LCM(48,14,40) = ( 48 × 14 × 40 ) / 16
LCM(48,14,40) = 26880 / 16
LCM(48,14,40) = 1680
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FAQs on GCF of Fractions of 353/48, 648/14, 289/40
1. What is the HCF of 353,648,289?
The HCF of 353,648,289 is 1
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 353/48, 648/14, 289/40?
Answer: GCF of Numerators as per given numbers 353/48, 648/14, 289/40 is
GCF of Numerators i.e. for 353,648,289 is 1
LCM of denominators i.e. for 48,14,40 is 1680.
Thus, GCF of Fractions is 1/1680.Finally, GCF of Fractions for 353/48, 648/14, 289/40 is 1/1680.