GCF of 159/266, 288/217
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 159/266, 288/217 i.e 3/8246 easily. The following is the detailed procedure to determine the greatest common factor of fractions 159/266, 288/217.
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 159/266,288/217?
Given fractions are 159/266,288/217
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 159/266,288/217, numerators are 159,288
Denominators are 266,217
The GCF of 159,288 is 3 .
LCM of 266,217 is 8246.
The greatest common factor of 159/266,288/217 = [GCF of 159,288]/[LCM of 266,217]= 3/8246
Therefore, the GCF of 159/266,288/217 is 3/8246.
To find the highest common factor of 159,288, we have to find the factors of both numbers and list the highest common factor.
The factors of 159 are 1, 3, 53, 159
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 159,288 is 3.
Lets's calculate GCF of 159,288
| 3 | 159, 288 |
| 53, 96 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 159,288 By Matching Biggest Common Factor Method
Now, list down the factors of 159
:1,3,53,159
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 159,288 . The biggest common factor number is the GCF number.
So the greatest common factor 159,288 is 3.
Lets's calculate LCM of 266,217
| 7 | 266, 217 |
| 38, 31 |
∴ So the LCM of the given numbers is 7 x 38 x 31 = 8246
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8246
Therefore, the GCF of Fractions 159/266,288/217 is 3/8246
Least Common Multiple of 266,217 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 266,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(266,217) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(266,217) x common factors =7 x 1 = 7
LCM(266,217) = ( 266 × 217 ) / 7
LCM(266,217) = 57722 / 7
LCM(266,217) = 8246
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FAQs on GCF of Fractions of 159/266, 288/217
1. What is the HCF of 159,288?
The HCF of 159,288 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 159/266, 288/217?
Answer: GCF of Numerators as per given numbers 159/266, 288/217 is
GCF of Numerators i.e. for 159,288 is 3
LCM of denominators i.e. for 266,217 is 8246.
Thus, GCF of Fractions is 3/8246.Finally, GCF of Fractions for 159/266, 288/217 is 3/8246.