How to Find GCF of 38/57, 976/14, 227/78?

GCF of 38/57, 976/14, 227/78

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 38/57, 976/14, 227/78 i.e 1/10374 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/57, 976/14, 227/78.

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 38/57,976/14,227/78?

Given fractions are 38/57,976/14,227/78

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 38/57,976/14,227/78, numerators are 38,976,227

Denominators are 57,14,78

The GCF of 38,976,227 is 1 .

LCM of 57,14,78 is 10374.

The greatest common factor of 38/57,976/14,227/78 = [GCF of 38,976,227]/[LCM of 57,14,78]= 1/10374

Therefore, the GCF of 38/57,976/14,227/78 is 1/10374.

Greatest Common Factor of 38,976,227

To find the highest common factor of 38,976,227, 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 976 are 1, 2, 4, 8, 16, 61, 122, 244, 488, 976

The factors of 227 are 1, 227

The HCF of 38,976,227 is 1.

Lets's calculate GCF of 38,976,227

Greatest Common Factor (GCF) of 38,976,227 By Common Division

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

Greatest Common Factor of 38,976,227 By Matching Biggest Common Factor Method

Now, list down the factors of 38

1,2,19,38

Now, list down the factors of 976

1,2,4,8,16,61,122,244,488,976

Now, list down the factors of 227

1,227

Greatest Common Factor

We found the factors 38,976,227 . The biggest common factor number is the GCF number.
So the greatest common factor 38,976,227 is 1.

Lets's calculate LCM of 57,14,78

Lowest Common Multiple of 57,14,78 using Common Division

2	57, 14, 78
3	57, 7, 39
	19, 7, 13

∴ So the LCM of the given numbers is 2 x 3 x 19 x 7 x 13 = 10374

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10374

Therefore, the GCF of Fractions 38/57,976/14,227/78 is 1/10374

Least Common Multiple of 57,14,78 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 57,14,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(57,14,78) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(57,14,78) x common factors =1 x 6 = 6

LCM(57,14,78) = ( 57 × 14 × 78 ) / 6

LCM(57,14,78) = 62244 / 6

LCM(57,14,78) = 10374

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FAQs on GCF of Fractions of 38/57, 976/14, 227/78

1. What is the HCF of 38,976,227?

The HCF of 38,976,227 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 38/57, 976/14, 227/78?

Answer: GCF of Numerators as per given numbers 38/57, 976/14, 227/78 is

GCF of Numerators i.e. for 38,976,227 is 1

LCM of denominators i.e. for 57,14,78 is 10374.

Thus, GCF of Fractions is 1/10374.Finally, GCF of Fractions for 38/57, 976/14, 227/78 is 1/10374.