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GCF of 469/89, 658/205

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 469/89, 658/205 i.e 7/18245 easily. The following is the detailed procedure to determine the greatest common factor of fractions 469/89, 658/205.

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 469/89,658/205?

Given fractions are 469/89,658/205

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 469/89,658/205, numerators are 469,658

Denominators are 89,205

The GCF of 469,658 is 7 .

LCM of 89,205 is 18245.

The greatest common factor of 469/89,658/205 = [GCF of 469,658]/[LCM of 89,205]= 7/18245

Therefore, the GCF of 469/89,658/205 is 7/18245.

Greatest Common Factor of 469,658

To find the highest common factor of 469,658, we have to find the factors of both numbers and list the highest common factor.

The factors of 469 are 1, 7, 67, 469

The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658

The HCF of 469,658 is 7.

Lets's calculate GCF of 469,658

Greatest Common Factor (GCF) of 469,658 By Common Division

7 469, 658
67, 94

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 469,658 By Matching Biggest Common Factor Method

Greatest Common Factor of 469,658 By Matching Biggest Common Factor Method

Now, list down the factors of 469

:

1,7,67,469

Now, list down the factors of 658

:

1,2,7,14,47,94,329,658

Greatest Common Factor

We found the factors 469,658 . The biggest common factor number is the GCF number.
So the greatest common factor 469,658 is 7.

Lets's calculate LCM of 89,205

Lowest Common Multiple of 89,205 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 18245

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/18245

Therefore, the GCF of Fractions 469/89,658/205 is 7/18245

Least Common Multiple of 89,205 with GCF Formula

Least Common Multiple of 89,205 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 89,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(89,205) = 1

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

GCF(89,205) x common factors =1 x 1 = 1

LCM(89,205) = ( 89 × 205 ) / 1

LCM(89,205) = 18245 / 1

LCM(89,205) = 18245


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FAQs on GCF of Fractions of 469/89, 658/205

1. What is the HCF of 469,658?

The HCF of 469,658 is 7

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 469/89, 658/205?

Answer: GCF of Numerators as per given numbers 469/89, 658/205 is

GCF of Numerators i.e. for 469,658 is 7

LCM of denominators i.e. for 89,205 is 18245.

Thus, GCF of Fractions is 7/18245.Finally, GCF of Fractions for 469/89, 658/205 is 7/18245.