How to Find GCF of 42/19, 37/92, 874/978?

GCF of 42/19, 37/92, 874/978

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 42/19, 37/92, 874/978 i.e 1/854772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/19, 37/92, 874/978.

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 42/19,37/92,874/978?

Given fractions are 42/19,37/92,874/978

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 42/19,37/92,874/978, numerators are 42,37,874

Denominators are 19,92,978

The GCF of 42,37,874 is 1 .

LCM of 19,92,978 is 854772.

The greatest common factor of 42/19,37/92,874/978 = [GCF of 42,37,874]/[LCM of 19,92,978]= 1/854772

Therefore, the GCF of 42/19,37/92,874/978 is 1/854772.

Greatest Common Factor of 42,37,874

To find the highest common factor of 42,37,874, we have to find the factors of both numbers and list the highest common factor.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The factors of 37 are 1, 37

The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874

The HCF of 42,37,874 is 1.

Lets's calculate GCF of 42,37,874

Greatest Common Factor (GCF) of 42,37,874 By Common Division

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

Greatest Common Factor of 42,37,874 By Matching Biggest Common Factor Method

Now, list down the factors of 42

1,2,3,6,7,14,21,42

Now, list down the factors of 37

1,37

Now, list down the factors of 874

1,2,19,23,38,46,437,874

Greatest Common Factor

We found the factors 42,37,874 . The biggest common factor number is the GCF number.
So the greatest common factor 42,37,874 is 1.

Lets's calculate LCM of 19,92,978

Lowest Common Multiple of 19,92,978 using Common Division

2	19, 92, 978
	19, 46, 489

∴ So the LCM of the given numbers is 2 x 19 x 46 x 489 = 854772

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/854772

Therefore, the GCF of Fractions 42/19,37/92,874/978 is 1/854772

Least Common Multiple of 19,92,978 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 19,92,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(19,92,978) = 1

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

GCF(19,92,978) x common factors =1 x 2 = 2

LCM(19,92,978) = ( 19 × 92 × 978 ) / 2

LCM(19,92,978) = 1709544 / 2

LCM(19,92,978) = 854772

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 42/19, 37/92, 874/978

1. What is the HCF of 42,37,874?

The HCF of 42,37,874 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 42/19, 37/92, 874/978?

Answer: GCF of Numerators as per given numbers 42/19, 37/92, 874/978 is

GCF of Numerators i.e. for 42,37,874 is 1

LCM of denominators i.e. for 19,92,978 is 854772.

Thus, GCF of Fractions is 1/854772.Finally, GCF of Fractions for 42/19, 37/92, 874/978 is 1/854772.