How to Find GCF of 318/540, 406/590?

GCF of 318/540, 406/590

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 318/540, 406/590 i.e 2/31860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 318/540, 406/590.

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 318/540,406/590?

Given fractions are 318/540,406/590

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 318/540,406/590, numerators are 318,406

Denominators are 540,590

The GCF of 318,406 is 2 .

LCM of 540,590 is 31860.

The greatest common factor of 318/540,406/590 = [GCF of 318,406]/[LCM of 540,590]= 2/31860

Therefore, the GCF of 318/540,406/590 is 2/31860.

Greatest Common Factor of 318,406

To find the highest common factor of 318,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 318 are 1, 2, 3, 6, 53, 106, 159, 318

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 318,406 is 2.

Lets's calculate GCF of 318,406

Greatest Common Factor (GCF) of 318,406 By Common Division

2	318, 406
	159, 203

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

Greatest Common Factor of 318,406 By Matching Biggest Common Factor Method

Now, list down the factors of 318

1,2,3,6,53,106,159,318

Now, list down the factors of 406

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 318,406 . The biggest common factor number is the GCF number.
So the greatest common factor 318,406 is 2.

Lets's calculate LCM of 540,590

Lowest Common Multiple of 540,590 using Common Division

2	540, 590
5	270, 295
	54, 59

∴ So the LCM of the given numbers is 2 x 5 x 54 x 59 = 31860

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/31860

Therefore, the GCF of Fractions 318/540,406/590 is 2/31860

Least Common Multiple of 540,590 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 540,590 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(540,590) = 10

common factors(in case of two or more numbers have common factors) = 1

GCF(540,590) x common factors =10 x 1 = 10

LCM(540,590) = ( 540 × 590 ) / 10

LCM(540,590) = 318600 / 10

LCM(540,590) = 31860

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FAQs on GCF of Fractions of 318/540, 406/590

1. What is the HCF of 318,406?

The HCF of 318,406 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 318/540, 406/590?

Answer: GCF of Numerators as per given numbers 318/540, 406/590 is

GCF of Numerators i.e. for 318,406 is 2

LCM of denominators i.e. for 540,590 is 31860.

Thus, GCF of Fractions is 2/31860.Finally, GCF of Fractions for 318/540, 406/590 is 2/31860.