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GCF of 409/40, 412/352

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 409/40, 412/352 i.e 1/1760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/40, 412/352.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 409/40,412/352?

Given fractions are 409/40,412/352

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 409/40,412/352, numerators are 409,412

Denominators are 40,352

The GCF of 409,412 is 1 .

LCM of 40,352 is 1760.

The greatest common factor of 409/40,412/352 = [GCF of 409,412]/[LCM of 40,352]= 1/1760

Therefore, the GCF of 409/40,412/352 is 1/1760.

Greatest Common Factor of 409,412

To find the highest common factor of 409,412, we have to find the factors of both numbers and list the highest common factor.

The factors of 409 are 1, 409

The factors of 412 are 1, 2, 4, 103, 206, 412

The HCF of 409,412 is 1.

Lets's calculate GCF of 409,412

Greatest Common Factor (GCF) of 409,412 By Common Division

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

Greatest Common Factor of 409,412 By Matching Biggest Common Factor Method

Greatest Common Factor of 409,412 By Matching Biggest Common Factor Method

Now, list down the factors of 409

:

1,409

Now, list down the factors of 412

:

1,2,4,103,206,412

Greatest Common Factor

We found the factors 409,412 . The biggest common factor number is the GCF number.
So the greatest common factor 409,412 is 1.

Lets's calculate LCM of 40,352

Lowest Common Multiple of 40,352 using Common Division

2 40, 352
2 20, 176
2 10, 88
5, 44

∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 44 = 1760

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1760

Therefore, the GCF of Fractions 409/40,412/352 is 1/1760

Least Common Multiple of 40,352 with GCF Formula

Least Common Multiple of 40,352 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 40,352 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,352) = 8

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

GCF(40,352) x common factors =8 x 1 = 8

LCM(40,352) = ( 40 × 352 ) / 8

LCM(40,352) = 14080 / 8

LCM(40,352) = 1760


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FAQs on GCF of Fractions of 409/40, 412/352

1. What is the HCF of 409,412?

The HCF of 409,412 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 409/40, 412/352?

Answer: GCF of Numerators as per given numbers 409/40, 412/352 is

GCF of Numerators i.e. for 409,412 is 1

LCM of denominators i.e. for 40,352 is 1760.

Thus, GCF of Fractions is 1/1760.Finally, GCF of Fractions for 409/40, 412/352 is 1/1760.