GCF of 609/85, 288/221
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 609/85, 288/221 i.e 3/1105 easily. The following is the detailed procedure to determine the greatest common factor of fractions 609/85, 288/221.
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 609/85,288/221?
Given fractions are 609/85,288/221
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 609/85,288/221, numerators are 609,288
Denominators are 85,221
The GCF of 609,288 is 3 .
LCM of 85,221 is 1105.
The greatest common factor of 609/85,288/221 = [GCF of 609,288]/[LCM of 85,221]= 3/1105
Therefore, the GCF of 609/85,288/221 is 3/1105.
To find the highest common factor of 609,288, we have to find the factors of both numbers and list the highest common factor.
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
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 609,288 is 3.
Lets's calculate GCF of 609,288
| 3 | 609, 288 |
| 203, 96 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 609,288 By Matching Biggest Common Factor Method
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
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 609,288 . The biggest common factor number is the GCF number.
So the greatest common factor 609,288 is 3.
Lets's calculate LCM of 85,221
| 17 | 85, 221 |
| 5, 13 |
∴ So the LCM of the given numbers is 17 x 5 x 13 = 1105
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1105
Therefore, the GCF of Fractions 609/85,288/221 is 3/1105
Least Common Multiple of 85,221 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 85,221 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,221) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(85,221) x common factors =17 x 1 = 17
LCM(85,221) = ( 85 × 221 ) / 17
LCM(85,221) = 18785 / 17
LCM(85,221) = 1105
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FAQs on GCF of Fractions of 609/85, 288/221
1. What is the HCF of 609,288?
The HCF of 609,288 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 609/85, 288/221?
Answer: GCF of Numerators as per given numbers 609/85, 288/221 is
GCF of Numerators i.e. for 609,288 is 3
LCM of denominators i.e. for 85,221 is 1105.
Thus, GCF of Fractions is 3/1105.Finally, GCF of Fractions for 609/85, 288/221 is 3/1105.