How to Find GCF of 168/449, 728/144?

GCF of 168/449, 728/144

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 168/449, 728/144 i.e 56/64656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/449, 728/144.

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 168/449,728/144?

Given fractions are 168/449,728/144

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 168/449,728/144, numerators are 168,728

Denominators are 449,144

The GCF of 168,728 is 56 .

LCM of 449,144 is 64656.

The greatest common factor of 168/449,728/144 = [GCF of 168,728]/[LCM of 449,144]= 56/64656

Therefore, the GCF of 168/449,728/144 is 56/64656.

Greatest Common Factor of 168,728

To find the highest common factor of 168,728, we have to find the factors of both numbers and list the highest common factor.

The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

The HCF of 168,728 is 56.

Lets's calculate GCF of 168,728

Greatest Common Factor (GCF) of 168,728 By Common Division

2	168, 728
2	84, 364
2	42, 182
7	21, 91
	3, 13

∴ So the GCF of the given numbers is 2 x 2 x 2 x 7 = 56

Greatest Common Factor of 168,728 By Matching Biggest Common Factor Method

Now, list down the factors of 168

1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168

Now, list down the factors of 728

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

Greatest Common Factor

We found the factors 168,728 . The biggest common factor number is the GCF number.
So the greatest common factor 168,728 is 56.

Lets's calculate LCM of 449,144

Lowest Common Multiple of 449,144 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 64656

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 56/64656

Therefore, the GCF of Fractions 168/449,728/144 is 56/64656

Least Common Multiple of 449,144 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 449,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(449,144) = 1

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

GCF(449,144) x common factors =1 x 1 = 1

LCM(449,144) = ( 449 × 144 ) / 1

LCM(449,144) = 64656 / 1

LCM(449,144) = 64656

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FAQs on GCF of Fractions of 168/449, 728/144

1. What is the HCF of 168,728?

The HCF of 168,728 is 56

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 168/449, 728/144?

Answer: GCF of Numerators as per given numbers 168/449, 728/144 is

GCF of Numerators i.e. for 168,728 is 56

LCM of denominators i.e. for 449,144 is 64656.

Thus, GCF of Fractions is 56/64656.Finally, GCF of Fractions for 168/449, 728/144 is 56/64656.