GCF of 105/14, 477/53, 414/23
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 105/14, 477/53, 414/23 i.e 3/17066 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/14, 477/53, 414/23.
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 105/14,477/53,414/23?
Given fractions are 105/14,477/53,414/23
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 105/14,477/53,414/23, numerators are 105,477,414
Denominators are 14,53,23
The GCF of 105,477,414 is 3 .
LCM of 14,53,23 is 17066.
The greatest common factor of 105/14,477/53,414/23 = [GCF of 105,477,414]/[LCM of 14,53,23]= 3/17066
Therefore, the GCF of 105/14,477/53,414/23 is 3/17066.
To find the highest common factor of 105,477,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 477 are 1, 3, 9, 53, 159, 477
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 105,477,414 is 3.
Lets's calculate GCF of 105,477,414
| 3 | 105, 477, 414 |
| 35, 159, 138 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 105,477,414 By Matching Biggest Common Factor Method
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Now, list down the factors of 477
:1,3,9,53,159,477
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 105,477,414 . The biggest common factor number is the GCF number.
So the greatest common factor 105,477,414 is 3.
Lets's calculate LCM of 14,53,23
Given numbers has no common factors except 1. So, there LCM is their product i.e 17066
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/17066
Therefore, the GCF of Fractions 105/14,477/53,414/23 is 3/17066
Least Common Multiple of 14,53,23 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 14,53,23 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,53,23) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(14,53,23) x common factors =1 x 1 = 1
LCM(14,53,23) = ( 14 × 53 × 23 ) / 1
LCM(14,53,23) = 17066 / 1
LCM(14,53,23) = 17066
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FAQs on GCF of Fractions of 105/14, 477/53, 414/23
1. What is the HCF of 105,477,414?
The HCF of 105,477,414 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 105/14, 477/53, 414/23?
Answer: GCF of Numerators as per given numbers 105/14, 477/53, 414/23 is
GCF of Numerators i.e. for 105,477,414 is 3
LCM of denominators i.e. for 14,53,23 is 17066.
Thus, GCF of Fractions is 3/17066.Finally, GCF of Fractions for 105/14, 477/53, 414/23 is 3/17066.