How to Find GCF of 31/154, 58/232, 498/347?

GCF of 31/154, 58/232, 498/347

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 31/154, 58/232, 498/347 i.e 1/6198808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/154, 58/232, 498/347.

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 31/154,58/232,498/347?

Given fractions are 31/154,58/232,498/347

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 31/154,58/232,498/347, numerators are 31,58,498

Denominators are 154,232,347

The GCF of 31,58,498 is 1 .

LCM of 154,232,347 is 6198808.

The greatest common factor of 31/154,58/232,498/347 = [GCF of 31,58,498]/[LCM of 154,232,347]= 1/6198808

Therefore, the GCF of 31/154,58/232,498/347 is 1/6198808.

Greatest Common Factor of 31,58,498

To find the highest common factor of 31,58,498, 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 58 are 1, 2, 29, 58

The factors of 498 are 1, 2, 3, 6, 83, 166, 249, 498

The HCF of 31,58,498 is 1.

Lets's calculate GCF of 31,58,498

Greatest Common Factor (GCF) of 31,58,498 By Common Division

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

Greatest Common Factor of 31,58,498 By Matching Biggest Common Factor Method

Now, list down the factors of 31

1,31

Now, list down the factors of 58

1,2,29,58

Now, list down the factors of 498

1,2,3,6,83,166,249,498

Greatest Common Factor

We found the factors 31,58,498 . The biggest common factor number is the GCF number.
So the greatest common factor 31,58,498 is 1.

Lets's calculate LCM of 154,232,347

Lowest Common Multiple of 154,232,347 using Common Division

2	154, 232, 347
	77, 116, 347

∴ So the LCM of the given numbers is 2 x 77 x 116 x 347 = 6198808

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6198808

Therefore, the GCF of Fractions 31/154,58/232,498/347 is 1/6198808

Least Common Multiple of 154,232,347 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 154,232,347 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(154,232,347) = 1

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

GCF(154,232,347) x common factors =1 x 2 = 2

LCM(154,232,347) = ( 154 × 232 × 347 ) / 2

LCM(154,232,347) = 12397616 / 2

LCM(154,232,347) = 6198808

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FAQs on GCF of Fractions of 31/154, 58/232, 498/347

1. What is the HCF of 31,58,498?

The HCF of 31,58,498 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 31/154, 58/232, 498/347?

Answer: GCF of Numerators as per given numbers 31/154, 58/232, 498/347 is

GCF of Numerators i.e. for 31,58,498 is 1

LCM of denominators i.e. for 154,232,347 is 6198808.

Thus, GCF of Fractions is 1/6198808.Finally, GCF of Fractions for 31/154, 58/232, 498/347 is 1/6198808.