How to Find GCF of 342/23, 900/2032?

GCF of 342/23, 900/2032

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 342/23, 900/2032 i.e 18/46736 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/23, 900/2032.

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 342/23,900/2032?

Given fractions are 342/23,900/2032

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 342/23,900/2032, numerators are 342,900

Denominators are 23,2032

The GCF of 342,900 is 18 .

LCM of 23,2032 is 46736.

The greatest common factor of 342/23,900/2032 = [GCF of 342,900]/[LCM of 23,2032]= 18/46736

Therefore, the GCF of 342/23,900/2032 is 18/46736.

Greatest Common Factor of 342,900

To find the highest common factor of 342,900, we have to find the factors of both numbers and list the highest common factor.

The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342

The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900

The HCF of 342,900 is 18.

Lets's calculate GCF of 342,900

Greatest Common Factor (GCF) of 342,900 By Common Division

2	342, 900
3	171, 450
3	57, 150
	19, 50

∴ So the GCF of the given numbers is 2 x 3 x 3 = 18

Greatest Common Factor of 342,900 By Matching Biggest Common Factor Method

Now, list down the factors of 342

1,2,3,6,9,18,19,38,57,114,171,342

Now, list down the factors of 900

1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900

Greatest Common Factor

We found the factors 342,900 . The biggest common factor number is the GCF number.
So the greatest common factor 342,900 is 18.

Lets's calculate LCM of 23,2032

Lowest Common Multiple of 23,2032 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 46736

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/46736

Therefore, the GCF of Fractions 342/23,900/2032 is 18/46736

Least Common Multiple of 23,2032 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 23,2032 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,2032) = 1

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

GCF(23,2032) x common factors =1 x 1 = 1

LCM(23,2032) = ( 23 × 2032 ) / 1

LCM(23,2032) = 46736 / 1

LCM(23,2032) = 46736

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FAQs on GCF of Fractions of 342/23, 900/2032

1. What is the HCF of 342,900?

The HCF of 342,900 is 18

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 342/23, 900/2032?

Answer: GCF of Numerators as per given numbers 342/23, 900/2032 is

GCF of Numerators i.e. for 342,900 is 18

LCM of denominators i.e. for 23,2032 is 46736.

Thus, GCF of Fractions is 18/46736.Finally, GCF of Fractions for 342/23, 900/2032 is 18/46736.