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GCF of 409/578, 3614/1636

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 409/578, 3614/1636 i.e 1/472804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/578, 3614/1636.

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 409/578,3614/1636?

Given fractions are 409/578,3614/1636

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 409/578,3614/1636, numerators are 409,3614

Denominators are 578,1636

The GCF of 409,3614 is 1 .

LCM of 578,1636 is 472804.

The greatest common factor of 409/578,3614/1636 = [GCF of 409,3614]/[LCM of 578,1636]= 1/472804

Therefore, the GCF of 409/578,3614/1636 is 1/472804.

Greatest Common Factor of 409,3614

To find the highest common factor of 409,3614, 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 3614 are 1, 2, 13, 26, 139, 278, 1807, 3614

The HCF of 409,3614 is 1.

Lets's calculate GCF of 409,3614

Greatest Common Factor (GCF) of 409,3614 By Common Division

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

Greatest Common Factor of 409,3614 By Matching Biggest Common Factor Method

Greatest Common Factor of 409,3614 By Matching Biggest Common Factor Method

Now, list down the factors of 409

:

1,409

Now, list down the factors of 3614

:

1,2,13,26,139,278,1807,3614

Greatest Common Factor

We found the factors 409,3614 . The biggest common factor number is the GCF number.
So the greatest common factor 409,3614 is 1.

Lets's calculate LCM of 578,1636

Lowest Common Multiple of 578,1636 using Common Division

2 578, 1636
289, 818

∴ So the LCM of the given numbers is 2 x 289 x 818 = 472804

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/472804

Therefore, the GCF of Fractions 409/578,3614/1636 is 1/472804

Least Common Multiple of 578,1636 with GCF Formula

Least Common Multiple of 578,1636 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 578,1636 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(578,1636) = 2

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

GCF(578,1636) x common factors =2 x 1 = 2

LCM(578,1636) = ( 578 × 1636 ) / 2

LCM(578,1636) = 945608 / 2

LCM(578,1636) = 472804


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FAQs on GCF of Fractions of 409/578, 3614/1636

1. What is the HCF of 409,3614?

The HCF of 409,3614 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 409/578, 3614/1636?

Answer: GCF of Numerators as per given numbers 409/578, 3614/1636 is

GCF of Numerators i.e. for 409,3614 is 1

LCM of denominators i.e. for 578,1636 is 472804.

Thus, GCF of Fractions is 1/472804.Finally, GCF of Fractions for 409/578, 3614/1636 is 1/472804.