How to Find GCF of 448/16, 784/223?

GCF of 448/16, 784/223

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 448/16, 784/223 i.e 112/3568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 448/16, 784/223.

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 448/16,784/223?

Given fractions are 448/16,784/223

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 448/16,784/223, numerators are 448,784

Denominators are 16,223

The GCF of 448,784 is 112 .

LCM of 16,223 is 3568.

The greatest common factor of 448/16,784/223 = [GCF of 448,784]/[LCM of 16,223]= 112/3568

Therefore, the GCF of 448/16,784/223 is 112/3568.

Greatest Common Factor of 448,784

To find the highest common factor of 448,784, we have to find the factors of both numbers and list the highest common factor.

The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448

The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784

The HCF of 448,784 is 112.

Lets's calculate GCF of 448,784

Greatest Common Factor (GCF) of 448,784 By Common Division

2	448, 784
2	224, 392
2	112, 196
2	56, 98
7	28, 49
	4, 7

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 7 = 112

Greatest Common Factor of 448,784 By Matching Biggest Common Factor Method

Now, list down the factors of 448

1,2,4,7,8,14,16,28,32,56,64,112,224,448

Now, list down the factors of 784

1,2,4,7,8,14,16,28,49,56,98,112,196,392,784

Greatest Common Factor

We found the factors 448,784 . The biggest common factor number is the GCF number.
So the greatest common factor 448,784 is 112.

Lets's calculate LCM of 16,223

Lowest Common Multiple of 16,223 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3568

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 112/3568

Therefore, the GCF of Fractions 448/16,784/223 is 112/3568

Least Common Multiple of 16,223 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 16,223 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,223) = 1

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

GCF(16,223) x common factors =1 x 1 = 1

LCM(16,223) = ( 16 × 223 ) / 1

LCM(16,223) = 3568 / 1

LCM(16,223) = 3568

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FAQs on GCF of Fractions of 448/16, 784/223

1. What is the HCF of 448,784?

The HCF of 448,784 is 112

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 448/16, 784/223?

Answer: GCF of Numerators as per given numbers 448/16, 784/223 is

GCF of Numerators i.e. for 448,784 is 112

LCM of denominators i.e. for 16,223 is 3568.

Thus, GCF of Fractions is 112/3568.Finally, GCF of Fractions for 448/16, 784/223 is 112/3568.