How to Find GCF of 2192/537, 3824/614?

GCF of 2192/537, 3824/614

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 2192/537, 3824/614 i.e 16/329718 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2192/537, 3824/614.

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 2192/537,3824/614?

Given fractions are 2192/537,3824/614

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 2192/537,3824/614, numerators are 2192,3824

Denominators are 537,614

The GCF of 2192,3824 is 16 .

LCM of 537,614 is 329718.

The greatest common factor of 2192/537,3824/614 = [GCF of 2192,3824]/[LCM of 537,614]= 16/329718

Therefore, the GCF of 2192/537,3824/614 is 16/329718.

Greatest Common Factor of 2192,3824

To find the highest common factor of 2192,3824, we have to find the factors of both numbers and list the highest common factor.

The factors of 2192 are 1, 2, 4, 8, 16, 137, 274, 548, 1096, 2192

The factors of 3824 are 1, 2, 4, 8, 16, 239, 478, 956, 1912, 3824

The HCF of 2192,3824 is 16.

Lets's calculate GCF of 2192,3824

Greatest Common Factor (GCF) of 2192,3824 By Common Division

2	2192, 3824
2	1096, 1912
2	548, 956
2	274, 478
	137, 239

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 2192,3824 By Matching Biggest Common Factor Method

Now, list down the factors of 2192

1,2,4,8,16,137,274,548,1096,2192

Now, list down the factors of 3824

1,2,4,8,16,239,478,956,1912,3824

Greatest Common Factor

We found the factors 2192,3824 . The biggest common factor number is the GCF number.
So the greatest common factor 2192,3824 is 16.

Lets's calculate LCM of 537,614

Lowest Common Multiple of 537,614 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 329718

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/329718

Therefore, the GCF of Fractions 2192/537,3824/614 is 16/329718

Least Common Multiple of 537,614 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 537,614 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(537,614) = 1

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

GCF(537,614) x common factors =1 x 1 = 1

LCM(537,614) = ( 537 × 614 ) / 1

LCM(537,614) = 329718 / 1

LCM(537,614) = 329718

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FAQs on GCF of Fractions of 2192/537, 3824/614

1. What is the HCF of 2192,3824?

The HCF of 2192,3824 is 16

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 2192/537, 3824/614?

Answer: GCF of Numerators as per given numbers 2192/537, 3824/614 is

GCF of Numerators i.e. for 2192,3824 is 16

LCM of denominators i.e. for 537,614 is 329718.

Thus, GCF of Fractions is 16/329718.Finally, GCF of Fractions for 2192/537, 3824/614 is 16/329718.