How to Find GCF of 229/32, 549/8128?

GCF of 229/32, 549/8128

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 229/32, 549/8128 i.e 1/8128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 229/32, 549/8128.

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 229/32,549/8128?

Given fractions are 229/32,549/8128

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 229/32,549/8128, numerators are 229,549

Denominators are 32,8128

The GCF of 229,549 is 1 .

LCM of 32,8128 is 8128.

The greatest common factor of 229/32,549/8128 = [GCF of 229,549]/[LCM of 32,8128]= 1/8128

Therefore, the GCF of 229/32,549/8128 is 1/8128.

Greatest Common Factor of 229,549

To find the highest common factor of 229,549, we have to find the factors of both numbers and list the highest common factor.

The factors of 229 are 1, 229

The factors of 549 are 1, 3, 9, 61, 183, 549

The HCF of 229,549 is 1.

Lets's calculate GCF of 229,549

Greatest Common Factor (GCF) of 229,549 By Common Division

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

Greatest Common Factor of 229,549 By Matching Biggest Common Factor Method

Now, list down the factors of 229

1,229

Now, list down the factors of 549

1,3,9,61,183,549

Greatest Common Factor

We found the factors 229,549 . The biggest common factor number is the GCF number.
So the greatest common factor 229,549 is 1.

Lets's calculate LCM of 32,8128

Lowest Common Multiple of 32,8128 using Common Division

2	32, 8128
2	16, 4064
2	8, 2032
2	4, 1016
2	2, 508
	1, 254

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 1 x 254 = 8128

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8128

Therefore, the GCF of Fractions 229/32,549/8128 is 1/8128

Least Common Multiple of 32,8128 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 32,8128 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(32,8128) = 32

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

GCF(32,8128) x common factors =32 x 1 = 32

LCM(32,8128) = ( 32 × 8128 ) / 32

LCM(32,8128) = 260096 / 32

LCM(32,8128) = 8128

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FAQs on GCF of Fractions of 229/32, 549/8128

1. What is the HCF of 229,549?

The HCF of 229,549 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 229/32, 549/8128?

Answer: GCF of Numerators as per given numbers 229/32, 549/8128 is

GCF of Numerators i.e. for 229,549 is 1

LCM of denominators i.e. for 32,8128 is 8128.

Thus, GCF of Fractions is 1/8128.Finally, GCF of Fractions for 229/32, 549/8128 is 1/8128.