How to Find GCF of 30/54, 209/78, 906/654?

GCF of 30/54, 209/78, 906/654

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 30/54, 209/78, 906/654 i.e 1/76518 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/54, 209/78, 906/654.

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 30/54,209/78,906/654?

Given fractions are 30/54,209/78,906/654

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 30/54,209/78,906/654, numerators are 30,209,906

Denominators are 54,78,654

The GCF of 30,209,906 is 1 .

LCM of 54,78,654 is 76518.

The greatest common factor of 30/54,209/78,906/654 = [GCF of 30,209,906]/[LCM of 54,78,654]= 1/76518

Therefore, the GCF of 30/54,209/78,906/654 is 1/76518.

Greatest Common Factor of 30,209,906

To find the highest common factor of 30,209,906, 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 209 are 1, 11, 19, 209

The factors of 906 are 1, 2, 3, 6, 151, 302, 453, 906

The HCF of 30,209,906 is 1.

Lets's calculate GCF of 30,209,906

Greatest Common Factor (GCF) of 30,209,906 By Common Division

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

Greatest Common Factor of 30,209,906 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 209

1,11,19,209

Now, list down the factors of 906

1,2,3,6,151,302,453,906

Greatest Common Factor

We found the factors 30,209,906 . The biggest common factor number is the GCF number.
So the greatest common factor 30,209,906 is 1.

Lets's calculate LCM of 54,78,654

Lowest Common Multiple of 54,78,654 using Common Division

2	54, 78, 654
3	27, 39, 327
	9, 13, 109

∴ So the LCM of the given numbers is 2 x 3 x 9 x 13 x 109 = 76518

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/76518

Therefore, the GCF of Fractions 30/54,209/78,906/654 is 1/76518

Least Common Multiple of 54,78,654 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 54,78,654 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(54,78,654) = 6

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

GCF(54,78,654) x common factors =6 x 6 = 36

LCM(54,78,654) = ( 54 × 78 × 654 ) / 36

LCM(54,78,654) = 2754648 / 36

LCM(54,78,654) = 76518

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 30/54, 209/78, 906/654

1. What is the HCF of 30,209,906?

The HCF of 30,209,906 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 30/54, 209/78, 906/654?

Answer: GCF of Numerators as per given numbers 30/54, 209/78, 906/654 is

GCF of Numerators i.e. for 30,209,906 is 1

LCM of denominators i.e. for 54,78,654 is 76518.

Thus, GCF of Fractions is 1/76518.Finally, GCF of Fractions for 30/54, 209/78, 906/654 is 1/76518.