How to Find GCF of 413/304, 3120/296?

GCF of 413/304, 3120/296

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 413/304, 3120/296 i.e 1/11248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 413/304, 3120/296.

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 413/304,3120/296?

Given fractions are 413/304,3120/296

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 413/304,3120/296, numerators are 413,3120

Denominators are 304,296

The GCF of 413,3120 is 1 .

LCM of 304,296 is 11248.

The greatest common factor of 413/304,3120/296 = [GCF of 413,3120]/[LCM of 304,296]= 1/11248

Therefore, the GCF of 413/304,3120/296 is 1/11248.

Greatest Common Factor of 413,3120

To find the highest common factor of 413,3120, we have to find the factors of both numbers and list the highest common factor.

The factors of 413 are 1, 7, 59, 413

The factors of 3120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 39, 40, 48, 52, 60, 65, 78, 80, 104, 120, 130, 156, 195, 208, 240, 260, 312, 390, 520, 624, 780, 1040, 1560, 3120

The HCF of 413,3120 is 1.

Lets's calculate GCF of 413,3120

Greatest Common Factor (GCF) of 413,3120 By Common Division

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

Greatest Common Factor of 413,3120 By Matching Biggest Common Factor Method

Now, list down the factors of 413

1,7,59,413

Now, list down the factors of 3120

1,2,3,4,5,6,8,10,12,13,15,16,20,24,26,30,39,40,48,52,60,65,78,80,104,120,130,156,195,208,240,260,312,390,520,624,780,1040,1560,3120

Greatest Common Factor

We found the factors 413,3120 . The biggest common factor number is the GCF number.
So the greatest common factor 413,3120 is 1.

Lets's calculate LCM of 304,296

Lowest Common Multiple of 304,296 using Common Division

2	304, 296
2	152, 148
2	76, 74
	38, 37

∴ So the LCM of the given numbers is 2 x 2 x 2 x 38 x 37 = 11248

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11248

Therefore, the GCF of Fractions 413/304,3120/296 is 1/11248

Least Common Multiple of 304,296 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 304,296 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(304,296) = 8

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

GCF(304,296) x common factors =8 x 1 = 8

LCM(304,296) = ( 304 × 296 ) / 8

LCM(304,296) = 89984 / 8

LCM(304,296) = 11248

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 413/304, 3120/296

1. What is the HCF of 413,3120?

The HCF of 413,3120 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 413/304, 3120/296?

Answer: GCF of Numerators as per given numbers 413/304, 3120/296 is

GCF of Numerators i.e. for 413,3120 is 1

LCM of denominators i.e. for 304,296 is 11248.

Thus, GCF of Fractions is 1/11248.Finally, GCF of Fractions for 413/304, 3120/296 is 1/11248.