How to Find GCF of 31/37, 509/24, 415/434?

GCF of 31/37, 509/24, 415/434

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 31/37, 509/24, 415/434 i.e 1/192696 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/37, 509/24, 415/434.

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 31/37,509/24,415/434?

Given fractions are 31/37,509/24,415/434

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 31/37,509/24,415/434, numerators are 31,509,415

Denominators are 37,24,434

The GCF of 31,509,415 is 1 .

LCM of 37,24,434 is 192696.

The greatest common factor of 31/37,509/24,415/434 = [GCF of 31,509,415]/[LCM of 37,24,434]= 1/192696

Therefore, the GCF of 31/37,509/24,415/434 is 1/192696.

Greatest Common Factor of 31,509,415

To find the highest common factor of 31,509,415, 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 509 are 1, 509

The factors of 415 are 1, 5, 83, 415

The HCF of 31,509,415 is 1.

Lets's calculate GCF of 31,509,415

Greatest Common Factor (GCF) of 31,509,415 By Common Division

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

Greatest Common Factor of 31,509,415 By Matching Biggest Common Factor Method

Now, list down the factors of 31

1,31

Now, list down the factors of 509

1,509

Now, list down the factors of 415

1,5,83,415

Greatest Common Factor

We found the factors 31,509,415 . The biggest common factor number is the GCF number.
So the greatest common factor 31,509,415 is 1.

Lets's calculate LCM of 37,24,434

Lowest Common Multiple of 37,24,434 using Common Division

2	37, 24, 434
	37, 12, 217

∴ So the LCM of the given numbers is 2 x 37 x 12 x 217 = 192696

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/192696

Therefore, the GCF of Fractions 31/37,509/24,415/434 is 1/192696

Least Common Multiple of 37,24,434 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 37,24,434 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(37,24,434) = 1

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

GCF(37,24,434) x common factors =1 x 2 = 2

LCM(37,24,434) = ( 37 × 24 × 434 ) / 2

LCM(37,24,434) = 385392 / 2

LCM(37,24,434) = 192696

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 31/37, 509/24, 415/434

1. What is the HCF of 31,509,415?

The HCF of 31,509,415 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 31/37, 509/24, 415/434?

Answer: GCF of Numerators as per given numbers 31/37, 509/24, 415/434 is

GCF of Numerators i.e. for 31,509,415 is 1

LCM of denominators i.e. for 37,24,434 is 192696.

Thus, GCF of Fractions is 1/192696.Finally, GCF of Fractions for 31/37, 509/24, 415/434 is 1/192696.