How to Find GCF of 31/72, 502/86, 112/735?

GCF of 31/72, 502/86, 112/735

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 31/72, 502/86, 112/735 i.e 1/758520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/72, 502/86, 112/735.

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 31/72,502/86,112/735?

Given fractions are 31/72,502/86,112/735

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 31/72,502/86,112/735, numerators are 31,502,112

Denominators are 72,86,735

The GCF of 31,502,112 is 1 .

LCM of 72,86,735 is 758520.

The greatest common factor of 31/72,502/86,112/735 = [GCF of 31,502,112]/[LCM of 72,86,735]= 1/758520

Therefore, the GCF of 31/72,502/86,112/735 is 1/758520.

Greatest Common Factor of 31,502,112

To find the highest common factor of 31,502,112, 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 502 are 1, 2, 251, 502

The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

The HCF of 31,502,112 is 1.

Lets's calculate GCF of 31,502,112

Greatest Common Factor (GCF) of 31,502,112 By Common Division

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

Greatest Common Factor of 31,502,112 By Matching Biggest Common Factor Method

Now, list down the factors of 31

1,31

Now, list down the factors of 502

1,2,251,502

Now, list down the factors of 112

1,2,4,7,8,14,16,28,56,112

Greatest Common Factor

We found the factors 31,502,112 . The biggest common factor number is the GCF number.
So the greatest common factor 31,502,112 is 1.

Lets's calculate LCM of 72,86,735

Lowest Common Multiple of 72,86,735 using Common Division

2	72, 86, 735
3	36, 43, 735
	12, 43, 245

∴ So the LCM of the given numbers is 2 x 3 x 12 x 43 x 245 = 758520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/758520

Therefore, the GCF of Fractions 31/72,502/86,112/735 is 1/758520

Least Common Multiple of 72,86,735 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 72,86,735 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(72,86,735) = 1

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

GCF(72,86,735) x common factors =1 x 6 = 6

LCM(72,86,735) = ( 72 × 86 × 735 ) / 6

LCM(72,86,735) = 4551120 / 6

LCM(72,86,735) = 758520

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 31/72, 502/86, 112/735

1. What is the HCF of 31,502,112?

The HCF of 31,502,112 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 31/72, 502/86, 112/735?

Answer: GCF of Numerators as per given numbers 31/72, 502/86, 112/735 is

GCF of Numerators i.e. for 31,502,112 is 1

LCM of denominators i.e. for 72,86,735 is 758520.

Thus, GCF of Fractions is 1/758520.Finally, GCF of Fractions for 31/72, 502/86, 112/735 is 1/758520.