GCF of 69/166, 414/512
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 69/166, 414/512 i.e 69/42496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/166, 414/512.
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 69/166,414/512?
Given fractions are 69/166,414/512
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 69/166,414/512, numerators are 69,414
Denominators are 166,512
The GCF of 69,414 is 69 .
LCM of 166,512 is 42496.
The greatest common factor of 69/166,414/512 = [GCF of 69,414]/[LCM of 166,512]= 69/42496
Therefore, the GCF of 69/166,414/512 is 69/42496.
To find the highest common factor of 69,414, 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 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 69,414 is 69.
Lets's calculate GCF of 69,414
| 3 | 69, 414 |
| 23 | 23, 138 |
| 1, 6 |
∴ So the GCF of the given numbers is 3 x 23 = 69
Greatest Common Factor of 69,414 By Matching Biggest Common Factor Method
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 69,414 . The biggest common factor number is the GCF number.
So the greatest common factor 69,414 is 69.
Lets's calculate LCM of 166,512
| 2 | 166, 512 |
| 83, 256 |
∴ So the LCM of the given numbers is 2 x 83 x 256 = 42496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 69/42496
Therefore, the GCF of Fractions 69/166,414/512 is 69/42496
Least Common Multiple of 166,512 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 166,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(166,512) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(166,512) x common factors =2 x 1 = 2
LCM(166,512) = ( 166 × 512 ) / 2
LCM(166,512) = 84992 / 2
LCM(166,512) = 42496
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FAQs on GCF of Fractions of 69/166, 414/512
1. What is the HCF of 69,414?
The HCF of 69,414 is 69
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 69/166, 414/512?
Answer: GCF of Numerators as per given numbers 69/166, 414/512 is
GCF of Numerators i.e. for 69,414 is 69
LCM of denominators i.e. for 166,512 is 42496.
Thus, GCF of Fractions is 69/42496.Finally, GCF of Fractions for 69/166, 414/512 is 69/42496.