How to Find GCF of 30/67, 19/56, 761/78?

GCF of 30/67, 19/56, 761/78

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 30/67, 19/56, 761/78 i.e 1/146328 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/67, 19/56, 761/78.

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 30/67,19/56,761/78?

Given fractions are 30/67,19/56,761/78

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 30/67,19/56,761/78, numerators are 30,19,761

Denominators are 67,56,78

The GCF of 30,19,761 is 1 .

LCM of 67,56,78 is 146328.

The greatest common factor of 30/67,19/56,761/78 = [GCF of 30,19,761]/[LCM of 67,56,78]= 1/146328

Therefore, the GCF of 30/67,19/56,761/78 is 1/146328.

Greatest Common Factor of 30,19,761

To find the highest common factor of 30,19,761, we have to find the factors of both numbers and list the highest common factor.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 19 are 1, 19

The factors of 761 are 1, 761

The HCF of 30,19,761 is 1.

Lets's calculate GCF of 30,19,761

Greatest Common Factor (GCF) of 30,19,761 By Common Division

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

Greatest Common Factor of 30,19,761 By Matching Biggest Common Factor Method

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 19

1,19

Now, list down the factors of 761

1,761

Greatest Common Factor

We found the factors 30,19,761 . The biggest common factor number is the GCF number.
So the greatest common factor 30,19,761 is 1.

Lets's calculate LCM of 67,56,78

Lowest Common Multiple of 67,56,78 using Common Division

2	67, 56, 78
	67, 28, 39

∴ So the LCM of the given numbers is 2 x 67 x 28 x 39 = 146328

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/146328

Therefore, the GCF of Fractions 30/67,19/56,761/78 is 1/146328

Least Common Multiple of 67,56,78 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 67,56,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(67,56,78) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(67,56,78) x common factors =1 x 2 = 2

LCM(67,56,78) = ( 67 × 56 × 78 ) / 2

LCM(67,56,78) = 292656 / 2

LCM(67,56,78) = 146328

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FAQs on GCF of Fractions of 30/67, 19/56, 761/78

1. What is the HCF of 30,19,761?

The HCF of 30,19,761 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 30/67, 19/56, 761/78?

Answer: GCF of Numerators as per given numbers 30/67, 19/56, 761/78 is

GCF of Numerators i.e. for 30,19,761 is 1

LCM of denominators i.e. for 67,56,78 is 146328.

Thus, GCF of Fractions is 1/146328.Finally, GCF of Fractions for 30/67, 19/56, 761/78 is 1/146328.