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GCF of 578/64, 234/427

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 578/64, 234/427 i.e 2/27328 easily. The following is the detailed procedure to determine the greatest common factor of fractions 578/64, 234/427.

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 578/64,234/427?

Given fractions are 578/64,234/427

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 578/64,234/427, numerators are 578,234

Denominators are 64,427

The GCF of 578,234 is 2 .

LCM of 64,427 is 27328.

The greatest common factor of 578/64,234/427 = [GCF of 578,234]/[LCM of 64,427]= 2/27328

Therefore, the GCF of 578/64,234/427 is 2/27328.

Greatest Common Factor of 578,234

To find the highest common factor of 578,234, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234

The HCF of 578,234 is 2.

Lets's calculate GCF of 578,234

Greatest Common Factor (GCF) of 578,234 By Common Division

2 578, 234
289, 117

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

Greatest Common Factor of 578,234 By Matching Biggest Common Factor Method

Greatest Common Factor of 578,234 By Matching Biggest Common Factor Method

Now, list down the factors of 578

:

1,2,17,34,289,578

Now, list down the factors of 234

:

1,2,3,6,9,13,18,26,39,78,117,234

Greatest Common Factor

We found the factors 578,234 . The biggest common factor number is the GCF number.
So the greatest common factor 578,234 is 2.

Lets's calculate LCM of 64,427

Lowest Common Multiple of 64,427 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 27328

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/27328

Therefore, the GCF of Fractions 578/64,234/427 is 2/27328

Least Common Multiple of 64,427 with GCF Formula

Least Common Multiple of 64,427 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 64,427 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(64,427) = 1

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

GCF(64,427) x common factors =1 x 1 = 1

LCM(64,427) = ( 64 × 427 ) / 1

LCM(64,427) = 27328 / 1

LCM(64,427) = 27328


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FAQs on GCF of Fractions of 578/64, 234/427

1. What is the HCF of 578,234?

The HCF of 578,234 is 2

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 578/64, 234/427?

Answer: GCF of Numerators as per given numbers 578/64, 234/427 is

GCF of Numerators i.e. for 578,234 is 2

LCM of denominators i.e. for 64,427 is 27328.

Thus, GCF of Fractions is 2/27328.Finally, GCF of Fractions for 578/64, 234/427 is 2/27328.