How to Find GCF of 156/184, 224/209?

GCF of 156/184, 224/209

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 156/184, 224/209 i.e 4/38456 easily. The following is the detailed procedure to determine the greatest common factor of fractions 156/184, 224/209.

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 156/184,224/209?

Given fractions are 156/184,224/209

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 156/184,224/209, numerators are 156,224

Denominators are 184,209

The GCF of 156,224 is 4 .

LCM of 184,209 is 38456.

The greatest common factor of 156/184,224/209 = [GCF of 156,224]/[LCM of 184,209]= 4/38456

Therefore, the GCF of 156/184,224/209 is 4/38456.

Greatest Common Factor of 156,224

To find the highest common factor of 156,224, we have to find the factors of both numbers and list the highest common factor.

The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156

The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224

The HCF of 156,224 is 4.

Lets's calculate GCF of 156,224

Greatest Common Factor (GCF) of 156,224 By Common Division

2	156, 224
2	78, 112
	39, 56

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

Greatest Common Factor of 156,224 By Matching Biggest Common Factor Method

Now, list down the factors of 156

1,2,3,4,6,12,13,26,39,52,78,156

Now, list down the factors of 224

1,2,4,7,8,14,16,28,32,56,112,224

Greatest Common Factor

We found the factors 156,224 . The biggest common factor number is the GCF number.
So the greatest common factor 156,224 is 4.

Lets's calculate LCM of 184,209

Lowest Common Multiple of 184,209 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 38456

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/38456

Therefore, the GCF of Fractions 156/184,224/209 is 4/38456

Least Common Multiple of 184,209 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 184,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(184,209) = 1

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

GCF(184,209) x common factors =1 x 1 = 1

LCM(184,209) = ( 184 × 209 ) / 1

LCM(184,209) = 38456 / 1

LCM(184,209) = 38456

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FAQs on GCF of Fractions of 156/184, 224/209

1. What is the HCF of 156,224?

The HCF of 156,224 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 156/184, 224/209?

Answer: GCF of Numerators as per given numbers 156/184, 224/209 is

GCF of Numerators i.e. for 156,224 is 4

LCM of denominators i.e. for 184,209 is 38456.

Thus, GCF of Fractions is 4/38456.Finally, GCF of Fractions for 156/184, 224/209 is 4/38456.