How to Find GCF of 46/57, 184/31, 621/146?

GCF of 46/57, 184/31, 621/146

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 46/57, 184/31, 621/146 i.e 23/257982 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/57, 184/31, 621/146.

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 46/57,184/31,621/146?

Given fractions are 46/57,184/31,621/146

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 46/57,184/31,621/146, numerators are 46,184,621

Denominators are 57,31,146

The GCF of 46,184,621 is 23 .

LCM of 57,31,146 is 257982.

The greatest common factor of 46/57,184/31,621/146 = [GCF of 46,184,621]/[LCM of 57,31,146]= 23/257982

Therefore, the GCF of 46/57,184/31,621/146 is 23/257982.

Greatest Common Factor of 46,184,621

To find the highest common factor of 46,184,621, we have to find the factors of both numbers and list the highest common factor.

The factors of 46 are 1, 2, 23, 46

The factors of 184 are 1, 2, 4, 8, 23, 46, 92, 184

The factors of 621 are 1, 3, 9, 23, 27, 69, 207, 621

The HCF of 46,184,621 is 23.

Lets's calculate GCF of 46,184,621

Greatest Common Factor (GCF) of 46,184,621 By Common Division

23	46, 184, 621
	2, 8, 27

∴ So the GCF of the given numbers is 23 = 23

Greatest Common Factor of 46,184,621 By Matching Biggest Common Factor Method

Now, list down the factors of 46

1,2,23,46

Now, list down the factors of 184

1,2,4,8,23,46,92,184

Now, list down the factors of 621

1,3,9,23,27,69,207,621

Greatest Common Factor

We found the factors 46,184,621 . The biggest common factor number is the GCF number.
So the greatest common factor 46,184,621 is 23.

Lets's calculate LCM of 57,31,146

Lowest Common Multiple of 57,31,146 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 257982

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/257982

Therefore, the GCF of Fractions 46/57,184/31,621/146 is 23/257982

Least Common Multiple of 57,31,146 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 57,31,146 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(57,31,146) = 1

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

GCF(57,31,146) x common factors =1 x 1 = 1

LCM(57,31,146) = ( 57 × 31 × 146 ) / 1

LCM(57,31,146) = 257982 / 1

LCM(57,31,146) = 257982

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FAQs on GCF of Fractions of 46/57, 184/31, 621/146

1. What is the HCF of 46,184,621?

The HCF of 46,184,621 is 23

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 46/57, 184/31, 621/146?

Answer: GCF of Numerators as per given numbers 46/57, 184/31, 621/146 is

GCF of Numerators i.e. for 46,184,621 is 23

LCM of denominators i.e. for 57,31,146 is 257982.

Thus, GCF of Fractions is 23/257982.Finally, GCF of Fractions for 46/57, 184/31, 621/146 is 23/257982.