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GCF of 165/33, 424/978

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 165/33, 424/978 i.e 1/10758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 165/33, 424/978.

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 165/33,424/978?

Given fractions are 165/33,424/978

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 165/33,424/978, numerators are 165,424

Denominators are 33,978

The GCF of 165,424 is 1 .

LCM of 33,978 is 10758.

The greatest common factor of 165/33,424/978 = [GCF of 165,424]/[LCM of 33,978]= 1/10758

Therefore, the GCF of 165/33,424/978 is 1/10758.

Greatest Common Factor of 165,424

To find the highest common factor of 165,424, we have to find the factors of both numbers and list the highest common factor.

The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165

The factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424

The HCF of 165,424 is 1.

Lets's calculate GCF of 165,424

Greatest Common Factor (GCF) of 165,424 By Common Division

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

Greatest Common Factor of 165,424 By Matching Biggest Common Factor Method

Greatest Common Factor of 165,424 By Matching Biggest Common Factor Method

Now, list down the factors of 165

:

1,3,5,11,15,33,55,165

Now, list down the factors of 424

:

1,2,4,8,53,106,212,424

Greatest Common Factor

We found the factors 165,424 . The biggest common factor number is the GCF number.
So the greatest common factor 165,424 is 1.

Lets's calculate LCM of 33,978

Lowest Common Multiple of 33,978 using Common Division

3 33, 978
11, 326

∴ So the LCM of the given numbers is 3 x 11 x 326 = 10758

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10758

Therefore, the GCF of Fractions 165/33,424/978 is 1/10758

Least Common Multiple of 33,978 with GCF Formula

Least Common Multiple of 33,978 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 33,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(33,978) = 3

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

GCF(33,978) x common factors =3 x 1 = 3

LCM(33,978) = ( 33 × 978 ) / 3

LCM(33,978) = 32274 / 3

LCM(33,978) = 10758


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 165/33, 424/978

1. What is the HCF of 165,424?

The HCF of 165,424 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 165/33, 424/978?

Answer: GCF of Numerators as per given numbers 165/33, 424/978 is

GCF of Numerators i.e. for 165,424 is 1

LCM of denominators i.e. for 33,978 is 10758.

Thus, GCF of Fractions is 1/10758.Finally, GCF of Fractions for 165/33, 424/978 is 1/10758.