How to Find GCF of 280/13, 414/2260?

GCF of 280/13, 414/2260

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 280/13, 414/2260 i.e 2/29380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 280/13, 414/2260.

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 280/13,414/2260?

Given fractions are 280/13,414/2260

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 280/13,414/2260, numerators are 280,414

Denominators are 13,2260

The GCF of 280,414 is 2 .

LCM of 13,2260 is 29380.

The greatest common factor of 280/13,414/2260 = [GCF of 280,414]/[LCM of 13,2260]= 2/29380

Therefore, the GCF of 280/13,414/2260 is 2/29380.

Greatest Common Factor of 280,414

To find the highest common factor of 280,414, we have to find the factors of both numbers and list the highest common factor.

The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280

The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

The HCF of 280,414 is 2.

Lets's calculate GCF of 280,414

Greatest Common Factor (GCF) of 280,414 By Common Division

2	280, 414
	140, 207

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

Greatest Common Factor of 280,414 By Matching Biggest Common Factor Method

Now, list down the factors of 280

1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280

Now, list down the factors of 414

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 280,414 . The biggest common factor number is the GCF number.
So the greatest common factor 280,414 is 2.

Lets's calculate LCM of 13,2260

Lowest Common Multiple of 13,2260 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 29380

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/29380

Therefore, the GCF of Fractions 280/13,414/2260 is 2/29380

Least Common Multiple of 13,2260 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 13,2260 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,2260) = 1

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

GCF(13,2260) x common factors =1 x 1 = 1

LCM(13,2260) = ( 13 × 2260 ) / 1

LCM(13,2260) = 29380 / 1

LCM(13,2260) = 29380

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FAQs on GCF of Fractions of 280/13, 414/2260

1. What is the HCF of 280,414?

The HCF of 280,414 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 280/13, 414/2260?

Answer: GCF of Numerators as per given numbers 280/13, 414/2260 is

GCF of Numerators i.e. for 280,414 is 2

LCM of denominators i.e. for 13,2260 is 29380.

Thus, GCF of Fractions is 2/29380.Finally, GCF of Fractions for 280/13, 414/2260 is 2/29380.