How to Find GCF of 20/68, 29/24, 418/51?

GCF of 20/68, 29/24, 418/51

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 20/68, 29/24, 418/51 i.e 1/408 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/68, 29/24, 418/51.

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 20/68,29/24,418/51?

Given fractions are 20/68,29/24,418/51

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 20/68,29/24,418/51, numerators are 20,29,418

Denominators are 68,24,51

The GCF of 20,29,418 is 1 .

LCM of 68,24,51 is 408.

The greatest common factor of 20/68,29/24,418/51 = [GCF of 20,29,418]/[LCM of 68,24,51]= 1/408

Therefore, the GCF of 20/68,29/24,418/51 is 1/408.

Greatest Common Factor of 20,29,418

To find the highest common factor of 20,29,418, we have to find the factors of both numbers and list the highest common factor.

The factors of 20 are 1, 2, 4, 5, 10, 20

The factors of 29 are 1, 29

The factors of 418 are 1, 2, 11, 19, 22, 38, 209, 418

The HCF of 20,29,418 is 1.

Lets's calculate GCF of 20,29,418

Greatest Common Factor (GCF) of 20,29,418 By Common Division

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

Greatest Common Factor of 20,29,418 By Matching Biggest Common Factor Method

Now, list down the factors of 20

1,2,4,5,10,20

Now, list down the factors of 29

1,29

Now, list down the factors of 418

1,2,11,19,22,38,209,418

Greatest Common Factor

We found the factors 20,29,418 . The biggest common factor number is the GCF number.
So the greatest common factor 20,29,418 is 1.

Lets's calculate LCM of 68,24,51

Lowest Common Multiple of 68,24,51 using Common Division

2	68, 24, 51
2	34, 12, 51
3	17, 6, 51
17	17, 2, 17
	1, 2, 1

∴ So the LCM of the given numbers is 2 x 2 x 3 x 17 x 1 x 2 x 1 = 408

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/408

Therefore, the GCF of Fractions 20/68,29/24,418/51 is 1/408

Least Common Multiple of 68,24,51 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 68,24,51 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,24,51) = 1

common factors(in case of two or more numbers have common factors) = 204

GCF(68,24,51) x common factors =1 x 204 = 204

LCM(68,24,51) = ( 68 × 24 × 51 ) / 204

LCM(68,24,51) = 83232 / 204

LCM(68,24,51) = 408

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 20/68, 29/24, 418/51

1. What is the HCF of 20,29,418?

The HCF of 20,29,418 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 20/68, 29/24, 418/51?

Answer: GCF of Numerators as per given numbers 20/68, 29/24, 418/51 is

GCF of Numerators i.e. for 20,29,418 is 1

LCM of denominators i.e. for 68,24,51 is 408.

Thus, GCF of Fractions is 1/408.Finally, GCF of Fractions for 20/68, 29/24, 418/51 is 1/408.