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GCF of 469/300, 221/254

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 469/300, 221/254 i.e 1/38100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 469/300, 221/254.

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 469/300,221/254?

Given fractions are 469/300,221/254

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 469/300,221/254, numerators are 469,221

Denominators are 300,254

The GCF of 469,221 is 1 .

LCM of 300,254 is 38100.

The greatest common factor of 469/300,221/254 = [GCF of 469,221]/[LCM of 300,254]= 1/38100

Therefore, the GCF of 469/300,221/254 is 1/38100.

Greatest Common Factor of 469,221

To find the highest common factor of 469,221, 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 221 are 1, 13, 17, 221

The HCF of 469,221 is 1.

Lets's calculate GCF of 469,221

Greatest Common Factor (GCF) of 469,221 By Common Division

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

Greatest Common Factor of 469,221 By Matching Biggest Common Factor Method

Greatest Common Factor of 469,221 By Matching Biggest Common Factor Method

Now, list down the factors of 469

:

1,7,67,469

Now, list down the factors of 221

:

1,13,17,221

Greatest Common Factor

We found the factors 469,221 . The biggest common factor number is the GCF number.
So the greatest common factor 469,221 is 1.

Lets's calculate LCM of 300,254

Lowest Common Multiple of 300,254 using Common Division

2 300, 254
150, 127

∴ So the LCM of the given numbers is 2 x 150 x 127 = 38100

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38100

Therefore, the GCF of Fractions 469/300,221/254 is 1/38100

Least Common Multiple of 300,254 with GCF Formula

Least Common Multiple of 300,254 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 300,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(300,254) = 2

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

GCF(300,254) x common factors =2 x 1 = 2

LCM(300,254) = ( 300 × 254 ) / 2

LCM(300,254) = 76200 / 2

LCM(300,254) = 38100


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FAQs on GCF of Fractions of 469/300, 221/254

1. What is the HCF of 469,221?

The HCF of 469,221 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 469/300, 221/254?

Answer: GCF of Numerators as per given numbers 469/300, 221/254 is

GCF of Numerators i.e. for 469,221 is 1

LCM of denominators i.e. for 300,254 is 38100.

Thus, GCF of Fractions is 1/38100.Finally, GCF of Fractions for 469/300, 221/254 is 1/38100.