GCF of 288/172, 856/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 288/172, 856/814 i.e 8/70004 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/172, 856/814.
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 288/172,856/814?
Given fractions are 288/172,856/814
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 288/172,856/814, numerators are 288,856
Denominators are 172,814
The GCF of 288,856 is 8 .
LCM of 172,814 is 70004.
The greatest common factor of 288/172,856/814 = [GCF of 288,856]/[LCM of 172,814]= 8/70004
Therefore, the GCF of 288/172,856/814 is 8/70004.
To find the highest common factor of 288,856, we have to find the factors of both numbers and list the highest common factor.
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The factors of 856 are 1, 2, 4, 8, 107, 214, 428, 856
The HCF of 288,856 is 8.
Lets's calculate GCF of 288,856
| 2 | 288, 856 |
| 2 | 144, 428 |
| 2 | 72, 214 |
| 36, 107 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 288,856 By Matching Biggest Common Factor Method
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
Now, list down the factors of 856
:1,2,4,8,107,214,428,856
Greatest Common Factor
We found the factors 288,856 . The biggest common factor number is the GCF number.
So the greatest common factor 288,856 is 8.
Lets's calculate LCM of 172,814
| 2 | 172, 814 |
| 86, 407 |
∴ So the LCM of the given numbers is 2 x 86 x 407 = 70004
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/70004
Therefore, the GCF of Fractions 288/172,856/814 is 8/70004
Least Common Multiple of 172,814 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 172,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(172,814) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(172,814) x common factors =2 x 1 = 2
LCM(172,814) = ( 172 × 814 ) / 2
LCM(172,814) = 140008 / 2
LCM(172,814) = 70004
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FAQs on GCF of Fractions of 288/172, 856/814
1. What is the HCF of 288,856?
The HCF of 288,856 is 8
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 288/172, 856/814?
Answer: GCF of Numerators as per given numbers 288/172, 856/814 is
GCF of Numerators i.e. for 288,856 is 8
LCM of denominators i.e. for 172,814 is 70004.
Thus, GCF of Fractions is 8/70004.Finally, GCF of Fractions for 288/172, 856/814 is 8/70004.