How to Find GCF of 30/23, 514/65, 639/368?

GCF of 30/23, 514/65, 639/368

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 30/23, 514/65, 639/368 i.e 1/23920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/23, 514/65, 639/368.

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 30/23,514/65,639/368?

Given fractions are 30/23,514/65,639/368

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 30/23,514/65,639/368, numerators are 30,514,639

Denominators are 23,65,368

The GCF of 30,514,639 is 1 .

LCM of 23,65,368 is 23920.

The greatest common factor of 30/23,514/65,639/368 = [GCF of 30,514,639]/[LCM of 23,65,368]= 1/23920

Therefore, the GCF of 30/23,514/65,639/368 is 1/23920.

Greatest Common Factor of 30,514,639

To find the highest common factor of 30,514,639, 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 514 are 1, 2, 257, 514

The factors of 639 are 1, 3, 9, 71, 213, 639

The HCF of 30,514,639 is 1.

Lets's calculate GCF of 30,514,639

Greatest Common Factor (GCF) of 30,514,639 By Common Division

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

Greatest Common Factor of 30,514,639 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 514

1,2,257,514

Now, list down the factors of 639

1,3,9,71,213,639

Greatest Common Factor

We found the factors 30,514,639 . The biggest common factor number is the GCF number.
So the greatest common factor 30,514,639 is 1.

Lets's calculate LCM of 23,65,368

Lowest Common Multiple of 23,65,368 using Common Division

23	23, 65, 368
	1, 65, 16

∴ So the LCM of the given numbers is 23 x 1 x 65 x 16 = 23920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23920

Therefore, the GCF of Fractions 30/23,514/65,639/368 is 1/23920

Least Common Multiple of 23,65,368 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 23,65,368 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,65,368) = 1

common factors(in case of two or more numbers have common factors) = 23

GCF(23,65,368) x common factors =1 x 23 = 23

LCM(23,65,368) = ( 23 × 65 × 368 ) / 23

LCM(23,65,368) = 550160 / 23

LCM(23,65,368) = 23920

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FAQs on GCF of Fractions of 30/23, 514/65, 639/368

1. What is the HCF of 30,514,639?

The HCF of 30,514,639 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 30/23, 514/65, 639/368?

Answer: GCF of Numerators as per given numbers 30/23, 514/65, 639/368 is

GCF of Numerators i.e. for 30,514,639 is 1

LCM of denominators i.e. for 23,65,368 is 23920.

Thus, GCF of Fractions is 1/23920.Finally, GCF of Fractions for 30/23, 514/65, 639/368 is 1/23920.