GCF of 297/34, 567/208
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 297/34, 567/208 i.e 27/3536 easily. The following is the detailed procedure to determine the greatest common factor of fractions 297/34, 567/208.
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 297/34,567/208?
Given fractions are 297/34,567/208
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 297/34,567/208, numerators are 297,567
Denominators are 34,208
The GCF of 297,567 is 27 .
LCM of 34,208 is 3536.
The greatest common factor of 297/34,567/208 = [GCF of 297,567]/[LCM of 34,208]= 27/3536
Therefore, the GCF of 297/34,567/208 is 27/3536.
To find the highest common factor of 297,567, we have to find the factors of both numbers and list the highest common factor.
The factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567
The HCF of 297,567 is 27.
Lets's calculate GCF of 297,567
| 3 | 297, 567 |
| 3 | 99, 189 |
| 3 | 33, 63 |
| 11, 21 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 297,567 By Matching Biggest Common Factor Method
Now, list down the factors of 297
:1,3,9,11,27,33,99,297
Now, list down the factors of 567
:1,3,7,9,21,27,63,81,189,567
Greatest Common Factor
We found the factors 297,567 . The biggest common factor number is the GCF number.
So the greatest common factor 297,567 is 27.
Lets's calculate LCM of 34,208
| 2 | 34, 208 |
| 17, 104 |
∴ So the LCM of the given numbers is 2 x 17 x 104 = 3536
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/3536
Therefore, the GCF of Fractions 297/34,567/208 is 27/3536
Least Common Multiple of 34,208 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 34,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,208) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,208) x common factors =2 x 1 = 2
LCM(34,208) = ( 34 × 208 ) / 2
LCM(34,208) = 7072 / 2
LCM(34,208) = 3536
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FAQs on GCF of Fractions of 297/34, 567/208
1. What is the HCF of 297,567?
The HCF of 297,567 is 27
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 297/34, 567/208?
Answer: GCF of Numerators as per given numbers 297/34, 567/208 is
GCF of Numerators i.e. for 297,567 is 27
LCM of denominators i.e. for 34,208 is 3536.
Thus, GCF of Fractions is 27/3536.Finally, GCF of Fractions for 297/34, 567/208 is 27/3536.