GCF of 209/156, 9588/998
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 209/156, 9588/998 i.e 1/77844 easily. The following is the detailed procedure to determine the greatest common factor of fractions 209/156, 9588/998.
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 209/156,9588/998?
Given fractions are 209/156,9588/998
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 209/156,9588/998, numerators are 209,9588
Denominators are 156,998
The GCF of 209,9588 is 1 .
LCM of 156,998 is 77844.
The greatest common factor of 209/156,9588/998 = [GCF of 209,9588]/[LCM of 156,998]= 1/77844
Therefore, the GCF of 209/156,9588/998 is 1/77844.
To find the highest common factor of 209,9588, we have to find the factors of both numbers and list the highest common factor.
The factors of 209 are 1, 11, 19, 209
The factors of 9588 are 1, 2, 3, 4, 6, 12, 17, 34, 47, 51, 68, 94, 102, 141, 188, 204, 282, 564, 799, 1598, 2397, 3196, 4794, 9588
The HCF of 209,9588 is 1.
Lets's calculate GCF of 209,9588
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 209,9588 By Matching Biggest Common Factor Method
Now, list down the factors of 209
:1,11,19,209
Now, list down the factors of 9588
:1,2,3,4,6,12,17,34,47,51,68,94,102,141,188,204,282,564,799,1598,2397,3196,4794,9588
Greatest Common Factor
We found the factors 209,9588 . The biggest common factor number is the GCF number.
So the greatest common factor 209,9588 is 1.
Lets's calculate LCM of 156,998
| 2 | 156, 998 |
| 78, 499 |
∴ So the LCM of the given numbers is 2 x 78 x 499 = 77844
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/77844
Therefore, the GCF of Fractions 209/156,9588/998 is 1/77844
Least Common Multiple of 156,998 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 156,998 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(156,998) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(156,998) x common factors =2 x 1 = 2
LCM(156,998) = ( 156 × 998 ) / 2
LCM(156,998) = 155688 / 2
LCM(156,998) = 77844
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FAQs on GCF of Fractions of 209/156, 9588/998
1. What is the HCF of 209,9588?
The HCF of 209,9588 is 1
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 209/156, 9588/998?
Answer: GCF of Numerators as per given numbers 209/156, 9588/998 is
GCF of Numerators i.e. for 209,9588 is 1
LCM of denominators i.e. for 156,998 is 77844.
Thus, GCF of Fractions is 1/77844.Finally, GCF of Fractions for 209/156, 9588/998 is 1/77844.