How to Find GCF of 31/74, 46/75, 206/38?

GCF of 31/74, 46/75, 206/38

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 31/74, 46/75, 206/38 i.e 1/105450 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/74, 46/75, 206/38.

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 31/74,46/75,206/38?

Given fractions are 31/74,46/75,206/38

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 31/74,46/75,206/38, numerators are 31,46,206

Denominators are 74,75,38

The GCF of 31,46,206 is 1 .

LCM of 74,75,38 is 105450.

The greatest common factor of 31/74,46/75,206/38 = [GCF of 31,46,206]/[LCM of 74,75,38]= 1/105450

Therefore, the GCF of 31/74,46/75,206/38 is 1/105450.

Greatest Common Factor of 31,46,206

To find the highest common factor of 31,46,206, we have to find the factors of both numbers and list the highest common factor.

The factors of 31 are 1, 31

The factors of 46 are 1, 2, 23, 46

The factors of 206 are 1, 2, 103, 206

The HCF of 31,46,206 is 1.

Lets's calculate GCF of 31,46,206

Greatest Common Factor (GCF) of 31,46,206 By Common Division

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

Greatest Common Factor of 31,46,206 By Matching Biggest Common Factor Method

Now, list down the factors of 31

1,31

Now, list down the factors of 46

1,2,23,46

Now, list down the factors of 206

1,2,103,206

Greatest Common Factor

We found the factors 31,46,206 . The biggest common factor number is the GCF number.
So the greatest common factor 31,46,206 is 1.

Lets's calculate LCM of 74,75,38

Lowest Common Multiple of 74,75,38 using Common Division

2	74, 75, 38
	37, 75, 19

∴ So the LCM of the given numbers is 2 x 37 x 75 x 19 = 105450

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/105450

Therefore, the GCF of Fractions 31/74,46/75,206/38 is 1/105450

Least Common Multiple of 74,75,38 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 74,75,38 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(74,75,38) = 1

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

GCF(74,75,38) x common factors =1 x 2 = 2

LCM(74,75,38) = ( 74 × 75 × 38 ) / 2

LCM(74,75,38) = 210900 / 2

LCM(74,75,38) = 105450

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FAQs on GCF of Fractions of 31/74, 46/75, 206/38

1. What is the HCF of 31,46,206?

The HCF of 31,46,206 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 31/74, 46/75, 206/38?

Answer: GCF of Numerators as per given numbers 31/74, 46/75, 206/38 is

GCF of Numerators i.e. for 31,46,206 is 1

LCM of denominators i.e. for 74,75,38 is 105450.

Thus, GCF of Fractions is 1/105450.Finally, GCF of Fractions for 31/74, 46/75, 206/38 is 1/105450.