How to Find GCF of 21/328, 29/456, 407/168?

GCF of 21/328, 29/456, 407/168

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 21/328, 29/456, 407/168 i.e 1/130872 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/328, 29/456, 407/168.

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 21/328,29/456,407/168?

Given fractions are 21/328,29/456,407/168

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 21/328,29/456,407/168, numerators are 21,29,407

Denominators are 328,456,168

The GCF of 21,29,407 is 1 .

LCM of 328,456,168 is 130872.

The greatest common factor of 21/328,29/456,407/168 = [GCF of 21,29,407]/[LCM of 328,456,168]= 1/130872

Therefore, the GCF of 21/328,29/456,407/168 is 1/130872.

Greatest Common Factor of 21,29,407

To find the highest common factor of 21,29,407, we have to find the factors of both numbers and list the highest common factor.

The factors of 21 are 1, 3, 7, 21

The factors of 29 are 1, 29

The factors of 407 are 1, 11, 37, 407

The HCF of 21,29,407 is 1.

Lets's calculate GCF of 21,29,407

Greatest Common Factor (GCF) of 21,29,407 By Common Division

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

Greatest Common Factor of 21,29,407 By Matching Biggest Common Factor Method

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 29

1,29

Now, list down the factors of 407

1,11,37,407

Greatest Common Factor

We found the factors 21,29,407 . The biggest common factor number is the GCF number.
So the greatest common factor 21,29,407 is 1.

Lets's calculate LCM of 328,456,168

Lowest Common Multiple of 328,456,168 using Common Division

2	328, 456, 168
2	164, 228, 84
2	82, 114, 42
3	41, 57, 21
	41, 19, 7

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 41 x 19 x 7 = 130872

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/130872

Therefore, the GCF of Fractions 21/328,29/456,407/168 is 1/130872

Least Common Multiple of 328,456,168 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 328,456,168 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(328,456,168) = 8

common factors(in case of two or more numbers have common factors) = 24

GCF(328,456,168) x common factors =8 x 24 = 192

LCM(328,456,168) = ( 328 × 456 × 168 ) / 192

LCM(328,456,168) = 25127424 / 192

LCM(328,456,168) = 130872

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FAQs on GCF of Fractions of 21/328, 29/456, 407/168

1. What is the HCF of 21,29,407?

The HCF of 21,29,407 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 21/328, 29/456, 407/168?

Answer: GCF of Numerators as per given numbers 21/328, 29/456, 407/168 is

GCF of Numerators i.e. for 21,29,407 is 1

LCM of denominators i.e. for 328,456,168 is 130872.

Thus, GCF of Fractions is 1/130872.Finally, GCF of Fractions for 21/328, 29/456, 407/168 is 1/130872.