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GCF of 111/30, 578/458

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 111/30, 578/458 i.e 1/6870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 111/30, 578/458.

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 111/30,578/458?

Given fractions are 111/30,578/458

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 111/30,578/458, numerators are 111,578

Denominators are 30,458

The GCF of 111,578 is 1 .

LCM of 30,458 is 6870.

The greatest common factor of 111/30,578/458 = [GCF of 111,578]/[LCM of 30,458]= 1/6870

Therefore, the GCF of 111/30,578/458 is 1/6870.

Greatest Common Factor of 111,578

To find the highest common factor of 111,578, we have to find the factors of both numbers and list the highest common factor.

The factors of 111 are 1, 3, 37, 111

The factors of 578 are 1, 2, 17, 34, 289, 578

The HCF of 111,578 is 1.

Lets's calculate GCF of 111,578

Greatest Common Factor (GCF) of 111,578 By Common Division

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

Greatest Common Factor of 111,578 By Matching Biggest Common Factor Method

Greatest Common Factor of 111,578 By Matching Biggest Common Factor Method

Now, list down the factors of 111

:

1,3,37,111

Now, list down the factors of 578

:

1,2,17,34,289,578

Greatest Common Factor

We found the factors 111,578 . The biggest common factor number is the GCF number.
So the greatest common factor 111,578 is 1.

Lets's calculate LCM of 30,458

Lowest Common Multiple of 30,458 using Common Division

2 30, 458
15, 229

∴ So the LCM of the given numbers is 2 x 15 x 229 = 6870

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6870

Therefore, the GCF of Fractions 111/30,578/458 is 1/6870

Least Common Multiple of 30,458 with GCF Formula

Least Common Multiple of 30,458 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 30,458 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,458) = 2

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

GCF(30,458) x common factors =2 x 1 = 2

LCM(30,458) = ( 30 × 458 ) / 2

LCM(30,458) = 13740 / 2

LCM(30,458) = 6870


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FAQs on GCF of Fractions of 111/30, 578/458

1. What is the HCF of 111,578?

The HCF of 111,578 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 111/30, 578/458?

Answer: GCF of Numerators as per given numbers 111/30, 578/458 is

GCF of Numerators i.e. for 111,578 is 1

LCM of denominators i.e. for 30,458 is 6870.

Thus, GCF of Fractions is 1/6870.Finally, GCF of Fractions for 111/30, 578/458 is 1/6870.