How to Find GCF of 51/34, 28/33, 14/408?

GCF of 51/34, 28/33, 14/408

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 51/34, 28/33, 14/408 i.e 1/4488 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/34, 28/33, 14/408.

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 51/34,28/33,14/408?

Given fractions are 51/34,28/33,14/408

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 51/34,28/33,14/408, numerators are 51,28,14

Denominators are 34,33,408

The GCF of 51,28,14 is 1 .

LCM of 34,33,408 is 4488.

The greatest common factor of 51/34,28/33,14/408 = [GCF of 51,28,14]/[LCM of 34,33,408]= 1/4488

Therefore, the GCF of 51/34,28/33,14/408 is 1/4488.

Greatest Common Factor of 51,28,14

To find the highest common factor of 51,28,14, we have to find the factors of both numbers and list the highest common factor.

The factors of 51 are 1, 3, 17, 51

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 14 are 1, 2, 7, 14

The HCF of 51,28,14 is 1.

Lets's calculate GCF of 51,28,14

Greatest Common Factor (GCF) of 51,28,14 By Common Division

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

Greatest Common Factor of 51,28,14 By Matching Biggest Common Factor Method

Now, list down the factors of 51

1,3,17,51

Now, list down the factors of 28

1,2,4,7,14,28

Now, list down the factors of 14

1,2,7,14

Greatest Common Factor

We found the factors 51,28,14 . The biggest common factor number is the GCF number.
So the greatest common factor 51,28,14 is 1.

Lets's calculate LCM of 34,33,408

Lowest Common Multiple of 34,33,408 using Common Division

2	34, 33, 408
3	17, 33, 204
17	17, 11, 68
	1, 11, 4

∴ So the LCM of the given numbers is 2 x 3 x 17 x 1 x 11 x 4 = 4488

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4488

Therefore, the GCF of Fractions 51/34,28/33,14/408 is 1/4488

Least Common Multiple of 34,33,408 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 34,33,408 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,33,408) = 1

common factors(in case of two or more numbers have common factors) = 102

GCF(34,33,408) x common factors =1 x 102 = 102

LCM(34,33,408) = ( 34 × 33 × 408 ) / 102

LCM(34,33,408) = 457776 / 102

LCM(34,33,408) = 4488

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FAQs on GCF of Fractions of 51/34, 28/33, 14/408

1. What is the HCF of 51,28,14?

The HCF of 51,28,14 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 51/34, 28/33, 14/408?

Answer: GCF of Numerators as per given numbers 51/34, 28/33, 14/408 is

GCF of Numerators i.e. for 51,28,14 is 1

LCM of denominators i.e. for 34,33,408 is 4488.

Thus, GCF of Fractions is 1/4488.Finally, GCF of Fractions for 51/34, 28/33, 14/408 is 1/4488.