How to Find GCF of 8224/222, 8096/3202?

GCF of 8224/222, 8096/3202

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 8224/222, 8096/3202 i.e 32/355422 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8224/222, 8096/3202.

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 8224/222,8096/3202?

Given fractions are 8224/222,8096/3202

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 8224/222,8096/3202, numerators are 8224,8096

Denominators are 222,3202

The GCF of 8224,8096 is 32 .

LCM of 222,3202 is 355422.

The greatest common factor of 8224/222,8096/3202 = [GCF of 8224,8096]/[LCM of 222,3202]= 32/355422

Therefore, the GCF of 8224/222,8096/3202 is 32/355422.

Greatest Common Factor of 8224,8096

To find the highest common factor of 8224,8096, we have to find the factors of both numbers and list the highest common factor.

The factors of 8224 are 1, 2, 4, 8, 16, 32, 257, 514, 1028, 2056, 4112, 8224

The factors of 8096 are 1, 2, 4, 8, 11, 16, 22, 23, 32, 44, 46, 88, 92, 176, 184, 253, 352, 368, 506, 736, 1012, 2024, 4048, 8096

The HCF of 8224,8096 is 32.

Lets's calculate GCF of 8224,8096

Greatest Common Factor (GCF) of 8224,8096 By Common Division

2	8224, 8096
2	4112, 4048
2	2056, 2024
2	1028, 1012
2	514, 506
	257, 253

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32

Greatest Common Factor of 8224,8096 By Matching Biggest Common Factor Method

Now, list down the factors of 8224

1,2,4,8,16,32,257,514,1028,2056,4112,8224

Now, list down the factors of 8096

1,2,4,8,11,16,22,23,32,44,46,88,92,176,184,253,352,368,506,736,1012,2024,4048,8096

Greatest Common Factor

We found the factors 8224,8096 . The biggest common factor number is the GCF number.
So the greatest common factor 8224,8096 is 32.

Lets's calculate LCM of 222,3202

Lowest Common Multiple of 222,3202 using Common Division

2	222, 3202
	111, 1601

∴ So the LCM of the given numbers is 2 x 111 x 1601 = 355422

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/355422

Therefore, the GCF of Fractions 8224/222,8096/3202 is 32/355422

Least Common Multiple of 222,3202 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 222,3202 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(222,3202) = 2

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

GCF(222,3202) x common factors =2 x 1 = 2

LCM(222,3202) = ( 222 × 3202 ) / 2

LCM(222,3202) = 710844 / 2

LCM(222,3202) = 355422

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FAQs on GCF of Fractions of 8224/222, 8096/3202

1. What is the HCF of 8224,8096?

The HCF of 8224,8096 is 32

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 8224/222, 8096/3202?

Answer: GCF of Numerators as per given numbers 8224/222, 8096/3202 is

GCF of Numerators i.e. for 8224,8096 is 32

LCM of denominators i.e. for 222,3202 is 355422.

Thus, GCF of Fractions is 32/355422.Finally, GCF of Fractions for 8224/222, 8096/3202 is 32/355422.