How to Find GCF of 512/72, 928/546?

GCF of 512/72, 928/546

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 512/72, 928/546 i.e 32/6552 easily. The following is the detailed procedure to determine the greatest common factor of fractions 512/72, 928/546.

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 512/72,928/546?

Given fractions are 512/72,928/546

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 512/72,928/546, numerators are 512,928

Denominators are 72,546

The GCF of 512,928 is 32 .

LCM of 72,546 is 6552.

The greatest common factor of 512/72,928/546 = [GCF of 512,928]/[LCM of 72,546]= 32/6552

Therefore, the GCF of 512/72,928/546 is 32/6552.

Greatest Common Factor of 512,928

To find the highest common factor of 512,928, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 928 are 1, 2, 4, 8, 16, 29, 32, 58, 116, 232, 464, 928

The HCF of 512,928 is 32.

Lets's calculate GCF of 512,928

Greatest Common Factor (GCF) of 512,928 By Common Division

2	512, 928
2	256, 464
2	128, 232
2	64, 116
2	32, 58
	16, 29

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32

Greatest Common Factor of 512,928 By Matching Biggest Common Factor Method

Now, list down the factors of 512

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

Now, list down the factors of 928

1,2,4,8,16,29,32,58,116,232,464,928

Greatest Common Factor

We found the factors 512,928 . The biggest common factor number is the GCF number.
So the greatest common factor 512,928 is 32.

Lets's calculate LCM of 72,546

Lowest Common Multiple of 72,546 using Common Division

2	72, 546
3	36, 273
	12, 91

∴ So the LCM of the given numbers is 2 x 3 x 12 x 91 = 6552

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/6552

Therefore, the GCF of Fractions 512/72,928/546 is 32/6552

Least Common Multiple of 72,546 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 72,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(72,546) = 6

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

GCF(72,546) x common factors =6 x 1 = 6

LCM(72,546) = ( 72 × 546 ) / 6

LCM(72,546) = 39312 / 6

LCM(72,546) = 6552

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FAQs on GCF of Fractions of 512/72, 928/546

1. What is the HCF of 512,928?

The HCF of 512,928 is 32

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 512/72, 928/546?

Answer: GCF of Numerators as per given numbers 512/72, 928/546 is

GCF of Numerators i.e. for 512,928 is 32

LCM of denominators i.e. for 72,546 is 6552.

Thus, GCF of Fractions is 32/6552.Finally, GCF of Fractions for 512/72, 928/546 is 32/6552.