How to Find GCF of 30/16, 15/49, 506/998?

GCF of 30/16, 15/49, 506/998

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 30/16, 15/49, 506/998 i.e 1/391216 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/16, 15/49, 506/998.

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 30/16,15/49,506/998?

Given fractions are 30/16,15/49,506/998

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 30/16,15/49,506/998, numerators are 30,15,506

Denominators are 16,49,998

The GCF of 30,15,506 is 1 .

LCM of 16,49,998 is 391216.

The greatest common factor of 30/16,15/49,506/998 = [GCF of 30,15,506]/[LCM of 16,49,998]= 1/391216

Therefore, the GCF of 30/16,15/49,506/998 is 1/391216.

Greatest Common Factor of 30,15,506

To find the highest common factor of 30,15,506, 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 15 are 1, 3, 5, 15

The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506

The HCF of 30,15,506 is 1.

Lets's calculate GCF of 30,15,506

Greatest Common Factor (GCF) of 30,15,506 By Common Division

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

Greatest Common Factor of 30,15,506 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 15

1,3,5,15

Now, list down the factors of 506

1,2,11,22,23,46,253,506

Greatest Common Factor

We found the factors 30,15,506 . The biggest common factor number is the GCF number.
So the greatest common factor 30,15,506 is 1.

Lets's calculate LCM of 16,49,998

Lowest Common Multiple of 16,49,998 using Common Division

2	16, 49, 998
	8, 49, 499

∴ So the LCM of the given numbers is 2 x 8 x 49 x 499 = 391216

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/391216

Therefore, the GCF of Fractions 30/16,15/49,506/998 is 1/391216

Least Common Multiple of 16,49,998 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 16,49,998 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,49,998) = 1

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

GCF(16,49,998) x common factors =1 x 2 = 2

LCM(16,49,998) = ( 16 × 49 × 998 ) / 2

LCM(16,49,998) = 782432 / 2

LCM(16,49,998) = 391216

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 30/16, 15/49, 506/998

1. What is the HCF of 30,15,506?

The HCF of 30,15,506 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 30/16, 15/49, 506/998?

Answer: GCF of Numerators as per given numbers 30/16, 15/49, 506/998 is

GCF of Numerators i.e. for 30,15,506 is 1

LCM of denominators i.e. for 16,49,998 is 391216.

Thus, GCF of Fractions is 1/391216.Finally, GCF of Fractions for 30/16, 15/49, 506/998 is 1/391216.