How to Find GCF of 192/21, 404/584?

GCF of 192/21, 404/584

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 192/21, 404/584 i.e 4/12264 easily. The following is the detailed procedure to determine the greatest common factor of fractions 192/21, 404/584.

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 192/21,404/584?

Given fractions are 192/21,404/584

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 192/21,404/584, numerators are 192,404

Denominators are 21,584

The GCF of 192,404 is 4 .

LCM of 21,584 is 12264.

The greatest common factor of 192/21,404/584 = [GCF of 192,404]/[LCM of 21,584]= 4/12264

Therefore, the GCF of 192/21,404/584 is 4/12264.

Greatest Common Factor of 192,404

To find the highest common factor of 192,404, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 404 are 1, 2, 4, 101, 202, 404

The HCF of 192,404 is 4.

Lets's calculate GCF of 192,404

Greatest Common Factor (GCF) of 192,404 By Common Division

2	192, 404
2	96, 202
	48, 101

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 192,404 By Matching Biggest Common Factor Method

Now, list down the factors of 192

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

Now, list down the factors of 404

1,2,4,101,202,404

Greatest Common Factor

We found the factors 192,404 . The biggest common factor number is the GCF number.
So the greatest common factor 192,404 is 4.

Lets's calculate LCM of 21,584

Lowest Common Multiple of 21,584 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 12264

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/12264

Therefore, the GCF of Fractions 192/21,404/584 is 4/12264

Least Common Multiple of 21,584 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 21,584 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,584) = 1

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

GCF(21,584) x common factors =1 x 1 = 1

LCM(21,584) = ( 21 × 584 ) / 1

LCM(21,584) = 12264 / 1

LCM(21,584) = 12264

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FAQs on GCF of Fractions of 192/21, 404/584

1. What is the HCF of 192,404?

The HCF of 192,404 is 4

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 192/21, 404/584?

Answer: GCF of Numerators as per given numbers 192/21, 404/584 is

GCF of Numerators i.e. for 192,404 is 4

LCM of denominators i.e. for 21,584 is 12264.

Thus, GCF of Fractions is 4/12264.Finally, GCF of Fractions for 192/21, 404/584 is 4/12264.