How to Find GCF of 38/96, 49/42, 723/912?

GCF of 38/96, 49/42, 723/912

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 38/96, 49/42, 723/912 i.e 1/12768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/96, 49/42, 723/912.

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 38/96,49/42,723/912?

Given fractions are 38/96,49/42,723/912

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 38/96,49/42,723/912, numerators are 38,49,723

Denominators are 96,42,912

The GCF of 38,49,723 is 1 .

LCM of 96,42,912 is 12768.

The greatest common factor of 38/96,49/42,723/912 = [GCF of 38,49,723]/[LCM of 96,42,912]= 1/12768

Therefore, the GCF of 38/96,49/42,723/912 is 1/12768.

Greatest Common Factor of 38,49,723

To find the highest common factor of 38,49,723, we have to find the factors of both numbers and list the highest common factor.

The factors of 38 are 1, 2, 19, 38

The factors of 49 are 1, 7, 49

The factors of 723 are 1, 3, 241, 723

The HCF of 38,49,723 is 1.

Lets's calculate GCF of 38,49,723

Greatest Common Factor (GCF) of 38,49,723 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 38,49,723 By Matching Biggest Common Factor Method

Now, list down the factors of 38

1,2,19,38

Now, list down the factors of 49

1,7,49

Now, list down the factors of 723

1,3,241,723

Greatest Common Factor

We found the factors 38,49,723 . The biggest common factor number is the GCF number.
So the greatest common factor 38,49,723 is 1.

Lets's calculate LCM of 96,42,912

Lowest Common Multiple of 96,42,912 using Common Division

2	96, 42, 912
2	48, 21, 456
2	24, 21, 228
2	12, 21, 114
3	6, 21, 57
	2, 7, 19

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 2 x 7 x 19 = 12768

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12768

Therefore, the GCF of Fractions 38/96,49/42,723/912 is 1/12768

Least Common Multiple of 96,42,912 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 96,42,912 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(96,42,912) = 6

common factors(in case of two or more numbers have common factors) = 48

GCF(96,42,912) x common factors =6 x 48 = 288

LCM(96,42,912) = ( 96 × 42 × 912 ) / 288

LCM(96,42,912) = 3677184 / 288

LCM(96,42,912) = 12768

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 38/96, 49/42, 723/912

1. What is the HCF of 38,49,723?

The HCF of 38,49,723 is 1

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 38/96, 49/42, 723/912?

Answer: GCF of Numerators as per given numbers 38/96, 49/42, 723/912 is

GCF of Numerators i.e. for 38,49,723 is 1

LCM of denominators i.e. for 96,42,912 is 12768.

Thus, GCF of Fractions is 1/12768.Finally, GCF of Fractions for 38/96, 49/42, 723/912 is 1/12768.