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GCF of 232/192, 213/600

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 232/192, 213/600 i.e 1/4800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 232/192, 213/600.

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 232/192,213/600?

Given fractions are 232/192,213/600

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 232/192,213/600, numerators are 232,213

Denominators are 192,600

The GCF of 232,213 is 1 .

LCM of 192,600 is 4800.

The greatest common factor of 232/192,213/600 = [GCF of 232,213]/[LCM of 192,600]= 1/4800

Therefore, the GCF of 232/192,213/600 is 1/4800.

Greatest Common Factor of 232,213

To find the highest common factor of 232,213, we have to find the factors of both numbers and list the highest common factor.

The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232

The factors of 213 are 1, 3, 71, 213

The HCF of 232,213 is 1.

Lets's calculate GCF of 232,213

Greatest Common Factor (GCF) of 232,213 By Common Division

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

Greatest Common Factor of 232,213 By Matching Biggest Common Factor Method

Greatest Common Factor of 232,213 By Matching Biggest Common Factor Method

Now, list down the factors of 232

:

1,2,4,8,29,58,116,232

Now, list down the factors of 213

:

1,3,71,213

Greatest Common Factor

We found the factors 232,213 . The biggest common factor number is the GCF number.
So the greatest common factor 232,213 is 1.

Lets's calculate LCM of 192,600

Lowest Common Multiple of 192,600 using Common Division

2 192, 600
2 96, 300
2 48, 150
3 24, 75
8, 25

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 8 x 25 = 4800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4800

Therefore, the GCF of Fractions 232/192,213/600 is 1/4800

Least Common Multiple of 192,600 with GCF Formula

Least Common Multiple of 192,600 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 192,600 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(192,600) = 24

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

GCF(192,600) x common factors =24 x 1 = 24

LCM(192,600) = ( 192 × 600 ) / 24

LCM(192,600) = 115200 / 24

LCM(192,600) = 4800


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FAQs on GCF of Fractions of 232/192, 213/600

1. What is the HCF of 232,213?

The HCF of 232,213 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 232/192, 213/600?

Answer: GCF of Numerators as per given numbers 232/192, 213/600 is

GCF of Numerators i.e. for 232,213 is 1

LCM of denominators i.e. for 192,600 is 4800.

Thus, GCF of Fractions is 1/4800.Finally, GCF of Fractions for 232/192, 213/600 is 1/4800.