How to Find GCF of 33/16, 41/21, 105/46?

GCF of 33/16, 41/21, 105/46

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 33/16, 41/21, 105/46 i.e 1/7728 easily. The following is the detailed procedure to determine the greatest common factor of fractions 33/16, 41/21, 105/46.

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 33/16,41/21,105/46?

Given fractions are 33/16,41/21,105/46

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 33/16,41/21,105/46, numerators are 33,41,105

Denominators are 16,21,46

The GCF of 33,41,105 is 1 .

LCM of 16,21,46 is 7728.

The greatest common factor of 33/16,41/21,105/46 = [GCF of 33,41,105]/[LCM of 16,21,46]= 1/7728

Therefore, the GCF of 33/16,41/21,105/46 is 1/7728.

Greatest Common Factor of 33,41,105

To find the highest common factor of 33,41,105, we have to find the factors of both numbers and list the highest common factor.

The factors of 33 are 1, 3, 11, 33

The factors of 41 are 1, 41

The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105

The HCF of 33,41,105 is 1.

Lets's calculate GCF of 33,41,105

Greatest Common Factor (GCF) of 33,41,105 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 33,41,105 By Matching Biggest Common Factor Method

Now, list down the factors of 33

1,3,11,33

Now, list down the factors of 41

1,41

Now, list down the factors of 105

1,3,5,7,15,21,35,105

Greatest Common Factor

We found the factors 33,41,105 . The biggest common factor number is the GCF number.
So the greatest common factor 33,41,105 is 1.

Lets's calculate LCM of 16,21,46

Lowest Common Multiple of 16,21,46 using Common Division

2	16, 21, 46
	8, 21, 23

∴ So the LCM of the given numbers is 2 x 8 x 21 x 23 = 7728

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7728

Therefore, the GCF of Fractions 33/16,41/21,105/46 is 1/7728

Least Common Multiple of 16,21,46 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 16,21,46 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,21,46) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(16,21,46) x common factors =1 x 2 = 2

LCM(16,21,46) = ( 16 × 21 × 46 ) / 2

LCM(16,21,46) = 15456 / 2

LCM(16,21,46) = 7728

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FAQs on GCF of Fractions of 33/16, 41/21, 105/46

1. What is the HCF of 33,41,105?

The HCF of 33,41,105 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 33/16, 41/21, 105/46?

Answer: GCF of Numerators as per given numbers 33/16, 41/21, 105/46 is

GCF of Numerators i.e. for 33,41,105 is 1

LCM of denominators i.e. for 16,21,46 is 7728.

Thus, GCF of Fractions is 1/7728.Finally, GCF of Fractions for 33/16, 41/21, 105/46 is 1/7728.