GCF of 41/52, 214/16, 364/548
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 41/52, 214/16, 364/548 i.e 1/28496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 41/52, 214/16, 364/548.
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 41/52,214/16,364/548?
Given fractions are 41/52,214/16,364/548
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 41/52,214/16,364/548, numerators are 41,214,364
Denominators are 52,16,548
The GCF of 41,214,364 is 1 .
LCM of 52,16,548 is 28496.
The greatest common factor of 41/52,214/16,364/548 = [GCF of 41,214,364]/[LCM of 52,16,548]= 1/28496
Therefore, the GCF of 41/52,214/16,364/548 is 1/28496.
To find the highest common factor of 41,214,364, we have to find the factors of both numbers and list the highest common factor.
The factors of 41 are 1, 41
The factors of 214 are 1, 2, 107, 214
The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
The HCF of 41,214,364 is 1.
Lets's calculate GCF of 41,214,364
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 41,214,364 By Matching Biggest Common Factor Method
Now, list down the factors of 41
:1,41
Now, list down the factors of 214
:1,2,107,214
Now, list down the factors of 364
:1,2,4,7,13,14,26,28,52,91,182,364
Greatest Common Factor
We found the factors 41,214,364 . The biggest common factor number is the GCF number.
So the greatest common factor 41,214,364 is 1.
Lets's calculate LCM of 52,16,548
| 2 | 52, 16, 548 |
| 2 | 26, 8, 274 |
| 13, 4, 137 |
∴ So the LCM of the given numbers is 2 x 2 x 13 x 4 x 137 = 28496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28496
Therefore, the GCF of Fractions 41/52,214/16,364/548 is 1/28496
Least Common Multiple of 52,16,548 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 52,16,548 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(52,16,548) = 4
common factors(in case of two or more numbers have common factors) = 4
GCF(52,16,548) x common factors =4 x 4 = 16
LCM(52,16,548) = ( 52 × 16 × 548 ) / 16
LCM(52,16,548) = 455936 / 16
LCM(52,16,548) = 28496
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FAQs on GCF of Fractions of 41/52, 214/16, 364/548
1. What is the HCF of 41,214,364?
The HCF of 41,214,364 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 41/52, 214/16, 364/548?
Answer: GCF of Numerators as per given numbers 41/52, 214/16, 364/548 is
GCF of Numerators i.e. for 41,214,364 is 1
LCM of denominators i.e. for 52,16,548 is 28496.
Thus, GCF of Fractions is 1/28496.Finally, GCF of Fractions for 41/52, 214/16, 364/548 is 1/28496.