How to Find GCF of 30/68, 40/21, 58/402?

GCF of 30/68, 40/21, 58/402

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 30/68, 40/21, 58/402 i.e 2/95676 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/68, 40/21, 58/402.

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 30/68,40/21,58/402?

Given fractions are 30/68,40/21,58/402

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 30/68,40/21,58/402, numerators are 30,40,58

Denominators are 68,21,402

The GCF of 30,40,58 is 2 .

LCM of 68,21,402 is 95676.

The greatest common factor of 30/68,40/21,58/402 = [GCF of 30,40,58]/[LCM of 68,21,402]= 2/95676

Therefore, the GCF of 30/68,40/21,58/402 is 2/95676.

Greatest Common Factor of 30,40,58

To find the highest common factor of 30,40,58, we have to find the factors of both numbers and list the highest common factor.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

The factors of 58 are 1, 2, 29, 58

The HCF of 30,40,58 is 2.

Lets's calculate GCF of 30,40,58

Greatest Common Factor (GCF) of 30,40,58 By Common Division

2	30, 40, 58
	15, 20, 29

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 30,40,58 By Matching Biggest Common Factor Method

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 40

1,2,4,5,8,10,20,40

Now, list down the factors of 58

1,2,29,58

Greatest Common Factor

We found the factors 30,40,58 . The biggest common factor number is the GCF number.
So the greatest common factor 30,40,58 is 2.

Lets's calculate LCM of 68,21,402

Lowest Common Multiple of 68,21,402 using Common Division

2	68, 21, 402
3	34, 21, 201
	34, 7, 67

∴ So the LCM of the given numbers is 2 x 3 x 34 x 7 x 67 = 95676

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/95676

Therefore, the GCF of Fractions 30/68,40/21,58/402 is 2/95676

Least Common Multiple of 68,21,402 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 68,21,402 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,21,402) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(68,21,402) x common factors =1 x 6 = 6

LCM(68,21,402) = ( 68 × 21 × 402 ) / 6

LCM(68,21,402) = 574056 / 6

LCM(68,21,402) = 95676

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 30/68, 40/21, 58/402

1. What is the HCF of 30,40,58?

The HCF of 30,40,58 is 2

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 30/68, 40/21, 58/402?

Answer: GCF of Numerators as per given numbers 30/68, 40/21, 58/402 is

GCF of Numerators i.e. for 30,40,58 is 2

LCM of denominators i.e. for 68,21,402 is 95676.

Thus, GCF of Fractions is 2/95676.Finally, GCF of Fractions for 30/68, 40/21, 58/402 is 2/95676.