How to Find GCF of 180/687, 2499/824?

GCF of 180/687, 2499/824

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 180/687, 2499/824 i.e 3/566088 easily. The following is the detailed procedure to determine the greatest common factor of fractions 180/687, 2499/824.

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 180/687,2499/824?

Given fractions are 180/687,2499/824

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 180/687,2499/824, numerators are 180,2499

Denominators are 687,824

The GCF of 180,2499 is 3 .

LCM of 687,824 is 566088.

The greatest common factor of 180/687,2499/824 = [GCF of 180,2499]/[LCM of 687,824]= 3/566088

Therefore, the GCF of 180/687,2499/824 is 3/566088.

Greatest Common Factor of 180,2499

To find the highest common factor of 180,2499, we have to find the factors of both numbers and list the highest common factor.

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The factors of 2499 are 1, 3, 7, 17, 21, 49, 51, 119, 147, 357, 833, 2499

The HCF of 180,2499 is 3.

Lets's calculate GCF of 180,2499

Greatest Common Factor (GCF) of 180,2499 By Common Division

3	180, 2499
	60, 833

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 180,2499 By Matching Biggest Common Factor Method

Now, list down the factors of 180

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Now, list down the factors of 2499

1,3,7,17,21,49,51,119,147,357,833,2499

Greatest Common Factor

We found the factors 180,2499 . The biggest common factor number is the GCF number.
So the greatest common factor 180,2499 is 3.

Lets's calculate LCM of 687,824

Lowest Common Multiple of 687,824 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 566088

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/566088

Therefore, the GCF of Fractions 180/687,2499/824 is 3/566088

Least Common Multiple of 687,824 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 687,824 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(687,824) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(687,824) x common factors =1 x 1 = 1

LCM(687,824) = ( 687 × 824 ) / 1

LCM(687,824) = 566088 / 1

LCM(687,824) = 566088

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FAQs on GCF of Fractions of 180/687, 2499/824

1. What is the HCF of 180,2499?

The HCF of 180,2499 is 3

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 180/687, 2499/824?

Answer: GCF of Numerators as per given numbers 180/687, 2499/824 is

GCF of Numerators i.e. for 180,2499 is 3

LCM of denominators i.e. for 687,824 is 566088.

Thus, GCF of Fractions is 3/566088.Finally, GCF of Fractions for 180/687, 2499/824 is 3/566088.