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GCF of 205/35, 430/454

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 205/35, 430/454 i.e 5/15890 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/35, 430/454.

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 205/35,430/454?

Given fractions are 205/35,430/454

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 205/35,430/454, numerators are 205,430

Denominators are 35,454

The GCF of 205,430 is 5 .

LCM of 35,454 is 15890.

The greatest common factor of 205/35,430/454 = [GCF of 205,430]/[LCM of 35,454]= 5/15890

Therefore, the GCF of 205/35,430/454 is 5/15890.

Greatest Common Factor of 205,430

To find the highest common factor of 205,430, we have to find the factors of both numbers and list the highest common factor.

The factors of 205 are 1, 5, 41, 205

The factors of 430 are 1, 2, 5, 10, 43, 86, 215, 430

The HCF of 205,430 is 5.

Lets's calculate GCF of 205,430

Greatest Common Factor (GCF) of 205,430 By Common Division

5 205, 430
41, 86

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 205,430 By Matching Biggest Common Factor Method

Greatest Common Factor of 205,430 By Matching Biggest Common Factor Method

Now, list down the factors of 205

:

1,5,41,205

Now, list down the factors of 430

:

1,2,5,10,43,86,215,430

Greatest Common Factor

We found the factors 205,430 . The biggest common factor number is the GCF number.
So the greatest common factor 205,430 is 5.

Lets's calculate LCM of 35,454

Lowest Common Multiple of 35,454 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 15890

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/15890

Therefore, the GCF of Fractions 205/35,430/454 is 5/15890

Least Common Multiple of 35,454 with GCF Formula

Least Common Multiple of 35,454 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 35,454 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(35,454) = 1

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

GCF(35,454) x common factors =1 x 1 = 1

LCM(35,454) = ( 35 × 454 ) / 1

LCM(35,454) = 15890 / 1

LCM(35,454) = 15890


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FAQs on GCF of Fractions of 205/35, 430/454

1. What is the HCF of 205,430?

The HCF of 205,430 is 5

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 205/35, 430/454?

Answer: GCF of Numerators as per given numbers 205/35, 430/454 is

GCF of Numerators i.e. for 205,430 is 5

LCM of denominators i.e. for 35,454 is 15890.

Thus, GCF of Fractions is 5/15890.Finally, GCF of Fractions for 205/35, 430/454 is 5/15890.