How to Find GCF of 384/142, 324/375?

GCF of 384/142, 324/375

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 384/142, 324/375 i.e 12/53250 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/142, 324/375.

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 384/142,324/375?

Given fractions are 384/142,324/375

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 384/142,324/375, numerators are 384,324

Denominators are 142,375

The GCF of 384,324 is 12 .

LCM of 142,375 is 53250.

The greatest common factor of 384/142,324/375 = [GCF of 384,324]/[LCM of 142,375]= 12/53250

Therefore, the GCF of 384/142,324/375 is 12/53250.

Greatest Common Factor of 384,324

To find the highest common factor of 384,324, we have to find the factors of both numbers and list the highest common factor.

The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384

The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324

The HCF of 384,324 is 12.

Lets's calculate GCF of 384,324

Greatest Common Factor (GCF) of 384,324 By Common Division

2	384, 324
2	192, 162
3	96, 81
	32, 27

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 384,324 By Matching Biggest Common Factor Method

Now, list down the factors of 384

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384

Now, list down the factors of 324

1,2,3,4,6,9,12,18,27,36,54,81,108,162,324

Greatest Common Factor

We found the factors 384,324 . The biggest common factor number is the GCF number.
So the greatest common factor 384,324 is 12.

Lets's calculate LCM of 142,375

Lowest Common Multiple of 142,375 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 53250

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/53250

Therefore, the GCF of Fractions 384/142,324/375 is 12/53250

Least Common Multiple of 142,375 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 142,375 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(142,375) = 1

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

GCF(142,375) x common factors =1 x 1 = 1

LCM(142,375) = ( 142 × 375 ) / 1

LCM(142,375) = 53250 / 1

LCM(142,375) = 53250

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FAQs on GCF of Fractions of 384/142, 324/375

1. What is the HCF of 384,324?

The HCF of 384,324 is 12

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 384/142, 324/375?

Answer: GCF of Numerators as per given numbers 384/142, 324/375 is

GCF of Numerators i.e. for 384,324 is 12

LCM of denominators i.e. for 142,375 is 53250.

Thus, GCF of Fractions is 12/53250.Finally, GCF of Fractions for 384/142, 324/375 is 12/53250.