GCF of 704/16, 288/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 704/16, 288/678 i.e 32/5424 easily. The following is the detailed procedure to determine the greatest common factor of fractions 704/16, 288/678.
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 704/16,288/678?
Given fractions are 704/16,288/678
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 704/16,288/678, numerators are 704,288
Denominators are 16,678
The GCF of 704,288 is 32 .
LCM of 16,678 is 5424.
The greatest common factor of 704/16,288/678 = [GCF of 704,288]/[LCM of 16,678]= 32/5424
Therefore, the GCF of 704/16,288/678 is 32/5424.
To find the highest common factor of 704,288, we have to find the factors of both numbers and list the highest common factor.
The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The HCF of 704,288 is 32.
Lets's calculate GCF of 704,288
| 2 | 704, 288 |
| 2 | 352, 144 |
| 2 | 176, 72 |
| 2 | 88, 36 |
| 2 | 44, 18 |
| 22, 9 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 704,288 By Matching Biggest Common Factor Method
Now, list down the factors of 704
:1,2,4,8,11,16,22,32,44,64,88,176,352,704
Now, list down the factors of 288
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288
Greatest Common Factor
We found the factors 704,288 . The biggest common factor number is the GCF number.
So the greatest common factor 704,288 is 32.
Lets's calculate LCM of 16,678
| 2 | 16, 678 |
| 8, 339 |
∴ So the LCM of the given numbers is 2 x 8 x 339 = 5424
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/5424
Therefore, the GCF of Fractions 704/16,288/678 is 32/5424
Least Common Multiple of 16,678 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 16,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,678) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(16,678) x common factors =2 x 1 = 2
LCM(16,678) = ( 16 × 678 ) / 2
LCM(16,678) = 10848 / 2
LCM(16,678) = 5424
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FAQs on GCF of Fractions of 704/16, 288/678
1. What is the HCF of 704,288?
The HCF of 704,288 is 32
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 704/16, 288/678?
Answer: GCF of Numerators as per given numbers 704/16, 288/678 is
GCF of Numerators i.e. for 704,288 is 32
LCM of denominators i.e. for 16,678 is 5424.
Thus, GCF of Fractions is 32/5424.Finally, GCF of Fractions for 704/16, 288/678 is 32/5424.