How to Find GCF of 189/264, 512/928?

GCF of 189/264, 512/928

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 189/264, 512/928 i.e 1/30624 easily. The following is the detailed procedure to determine the greatest common factor of fractions 189/264, 512/928.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 189/264,512/928?

Given fractions are 189/264,512/928

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 189/264,512/928, numerators are 189,512

Denominators are 264,928

The GCF of 189,512 is 1 .

LCM of 264,928 is 30624.

The greatest common factor of 189/264,512/928 = [GCF of 189,512]/[LCM of 264,928]= 1/30624

Therefore, the GCF of 189/264,512/928 is 1/30624.

Greatest Common Factor of 189,512

To find the highest common factor of 189,512, we have to find the factors of both numbers and list the highest common factor.

The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The HCF of 189,512 is 1.

Lets's calculate GCF of 189,512

Greatest Common Factor (GCF) of 189,512 By Common Division

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

Greatest Common Factor of 189,512 By Matching Biggest Common Factor Method

Now, list down the factors of 189

1,3,7,9,21,27,63,189

Now, list down the factors of 512

1,2,4,8,16,32,64,128,256,512

Greatest Common Factor

We found the factors 189,512 . The biggest common factor number is the GCF number.
So the greatest common factor 189,512 is 1.

Lets's calculate LCM of 264,928

Lowest Common Multiple of 264,928 using Common Division

2	264, 928
2	132, 464
2	66, 232
	33, 116

∴ So the LCM of the given numbers is 2 x 2 x 2 x 33 x 116 = 30624

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30624

Therefore, the GCF of Fractions 189/264,512/928 is 1/30624

Least Common Multiple of 264,928 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 264,928 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(264,928) = 8

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

GCF(264,928) x common factors =8 x 1 = 8

LCM(264,928) = ( 264 × 928 ) / 8

LCM(264,928) = 244992 / 8

LCM(264,928) = 30624

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FAQs on GCF of Fractions of 189/264, 512/928

1. What is the HCF of 189,512?

The HCF of 189,512 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 189/264, 512/928?

Answer: GCF of Numerators as per given numbers 189/264, 512/928 is

GCF of Numerators i.e. for 189,512 is 1

LCM of denominators i.e. for 264,928 is 30624.

Thus, GCF of Fractions is 1/30624.Finally, GCF of Fractions for 189/264, 512/928 is 1/30624.