GCF of 69/109, 45/206, 406/136
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 69/109, 45/206, 406/136 i.e 1/1526872 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/109, 45/206, 406/136.
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 69/109,45/206,406/136?
Given fractions are 69/109,45/206,406/136
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 69/109,45/206,406/136, numerators are 69,45,406
Denominators are 109,206,136
The GCF of 69,45,406 is 1 .
LCM of 109,206,136 is 1526872.
The greatest common factor of 69/109,45/206,406/136 = [GCF of 69,45,406]/[LCM of 109,206,136]= 1/1526872
Therefore, the GCF of 69/109,45/206,406/136 is 1/1526872.
To find the highest common factor of 69,45,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 69 are 1, 3, 23, 69
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 69,45,406 is 1.
Lets's calculate GCF of 69,45,406
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 69,45,406 By Matching Biggest Common Factor Method
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 69,45,406 . The biggest common factor number is the GCF number.
So the greatest common factor 69,45,406 is 1.
Lets's calculate LCM of 109,206,136
| 2 | 109, 206, 136 |
| 109, 103, 68 |
∴ So the LCM of the given numbers is 2 x 109 x 103 x 68 = 1526872
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1526872
Therefore, the GCF of Fractions 69/109,45/206,406/136 is 1/1526872
Least Common Multiple of 109,206,136 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 109,206,136 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(109,206,136) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(109,206,136) x common factors =1 x 2 = 2
LCM(109,206,136) = ( 109 × 206 × 136 ) / 2
LCM(109,206,136) = 3053744 / 2
LCM(109,206,136) = 1526872
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FAQs on GCF of Fractions of 69/109, 45/206, 406/136
1. What is the HCF of 69,45,406?
The HCF of 69,45,406 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 69/109, 45/206, 406/136?
Answer: GCF of Numerators as per given numbers 69/109, 45/206, 406/136 is
GCF of Numerators i.e. for 69,45,406 is 1
LCM of denominators i.e. for 109,206,136 is 1526872.
Thus, GCF of Fractions is 1/1526872.Finally, GCF of Fractions for 69/109, 45/206, 406/136 is 1/1526872.