How to Find GCF of 592/223, 144/878?

GCF of 592/223, 144/878

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 592/223, 144/878 i.e 16/195794 easily. The following is the detailed procedure to determine the greatest common factor of fractions 592/223, 144/878.

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 592/223,144/878?

Given fractions are 592/223,144/878

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 592/223,144/878, numerators are 592,144

Denominators are 223,878

The GCF of 592,144 is 16 .

LCM of 223,878 is 195794.

The greatest common factor of 592/223,144/878 = [GCF of 592,144]/[LCM of 223,878]= 16/195794

Therefore, the GCF of 592/223,144/878 is 16/195794.

Greatest Common Factor of 592,144

To find the highest common factor of 592,144, we have to find the factors of both numbers and list the highest common factor.

The factors of 592 are 1, 2, 4, 8, 16, 37, 74, 148, 296, 592

The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

The HCF of 592,144 is 16.

Lets's calculate GCF of 592,144

Greatest Common Factor (GCF) of 592,144 By Common Division

2	592, 144
2	296, 72
2	148, 36
2	74, 18
	37, 9

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 592,144 By Matching Biggest Common Factor Method

Now, list down the factors of 592

1,2,4,8,16,37,74,148,296,592

Now, list down the factors of 144

1,2,3,4,6,8,9,12,16,18,24,36,48,72,144

Greatest Common Factor

We found the factors 592,144 . The biggest common factor number is the GCF number.
So the greatest common factor 592,144 is 16.

Lets's calculate LCM of 223,878

Lowest Common Multiple of 223,878 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 195794

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/195794

Therefore, the GCF of Fractions 592/223,144/878 is 16/195794

Least Common Multiple of 223,878 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 223,878 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(223,878) = 1

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

GCF(223,878) x common factors =1 x 1 = 1

LCM(223,878) = ( 223 × 878 ) / 1

LCM(223,878) = 195794 / 1

LCM(223,878) = 195794

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FAQs on GCF of Fractions of 592/223, 144/878

1. What is the HCF of 592,144?

The HCF of 592,144 is 16

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 592/223, 144/878?

Answer: GCF of Numerators as per given numbers 592/223, 144/878 is

GCF of Numerators i.e. for 592,144 is 16

LCM of denominators i.e. for 223,878 is 195794.

Thus, GCF of Fractions is 16/195794.Finally, GCF of Fractions for 592/223, 144/878 is 16/195794.