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GCF of 409/465, 109/355

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 409/465, 109/355 i.e 1/33015 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/465, 109/355.

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 409/465,109/355?

Given fractions are 409/465,109/355

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 409/465,109/355, numerators are 409,109

Denominators are 465,355

The GCF of 409,109 is 1 .

LCM of 465,355 is 33015.

The greatest common factor of 409/465,109/355 = [GCF of 409,109]/[LCM of 465,355]= 1/33015

Therefore, the GCF of 409/465,109/355 is 1/33015.

Greatest Common Factor of 409,109

To find the highest common factor of 409,109, 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 109 are 1, 109

The HCF of 409,109 is 1.

Lets's calculate GCF of 409,109

Greatest Common Factor (GCF) of 409,109 By Common Division

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

Greatest Common Factor of 409,109 By Matching Biggest Common Factor Method

Greatest Common Factor of 409,109 By Matching Biggest Common Factor Method

Now, list down the factors of 409

:

1,409

Now, list down the factors of 109

:

1,109

Greatest Common Factor

We found the factors 409,109 . The biggest common factor number is the GCF number.
So the greatest common factor 409,109 is 1.

Lets's calculate LCM of 465,355

Lowest Common Multiple of 465,355 using Common Division

5 465, 355
93, 71

∴ So the LCM of the given numbers is 5 x 93 x 71 = 33015

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/33015

Therefore, the GCF of Fractions 409/465,109/355 is 1/33015

Least Common Multiple of 465,355 with GCF Formula

Least Common Multiple of 465,355 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 465,355 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(465,355) = 5

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

GCF(465,355) x common factors =5 x 1 = 5

LCM(465,355) = ( 465 × 355 ) / 5

LCM(465,355) = 165075 / 5

LCM(465,355) = 33015


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FAQs on GCF of Fractions of 409/465, 109/355

1. What is the HCF of 409,109?

The HCF of 409,109 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 409/465, 109/355?

Answer: GCF of Numerators as per given numbers 409/465, 109/355 is

GCF of Numerators i.e. for 409,109 is 1

LCM of denominators i.e. for 465,355 is 33015.

Thus, GCF of Fractions is 1/33015.Finally, GCF of Fractions for 409/465, 109/355 is 1/33015.