How to Find GCF of 864/12, 522/7562?

GCF of 864/12, 522/7562

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 864/12, 522/7562 i.e 18/45372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 864/12, 522/7562.

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 864/12,522/7562?

Given fractions are 864/12,522/7562

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 864/12,522/7562, numerators are 864,522

Denominators are 12,7562

The GCF of 864,522 is 18 .

LCM of 12,7562 is 45372.

The greatest common factor of 864/12,522/7562 = [GCF of 864,522]/[LCM of 12,7562]= 18/45372

Therefore, the GCF of 864/12,522/7562 is 18/45372.

Greatest Common Factor of 864,522

To find the highest common factor of 864,522, we have to find the factors of both numbers and list the highest common factor.

The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864

The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522

The HCF of 864,522 is 18.

Lets's calculate GCF of 864,522

Greatest Common Factor (GCF) of 864,522 By Common Division

2	864, 522
3	432, 261
3	144, 87
	48, 29

∴ So the GCF of the given numbers is 2 x 3 x 3 = 18

Greatest Common Factor of 864,522 By Matching Biggest Common Factor Method

Now, list down the factors of 864

1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864

Now, list down the factors of 522

1,2,3,6,9,18,29,58,87,174,261,522

Greatest Common Factor

We found the factors 864,522 . The biggest common factor number is the GCF number.
So the greatest common factor 864,522 is 18.

Lets's calculate LCM of 12,7562

Lowest Common Multiple of 12,7562 using Common Division

2	12, 7562
	6, 3781

∴ So the LCM of the given numbers is 2 x 6 x 3781 = 45372

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/45372

Therefore, the GCF of Fractions 864/12,522/7562 is 18/45372

Least Common Multiple of 12,7562 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 12,7562 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,7562) = 2

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

GCF(12,7562) x common factors =2 x 1 = 2

LCM(12,7562) = ( 12 × 7562 ) / 2

LCM(12,7562) = 90744 / 2

LCM(12,7562) = 45372

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FAQs on GCF of Fractions of 864/12, 522/7562

1. What is the HCF of 864,522?

The HCF of 864,522 is 18

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 864/12, 522/7562?

Answer: GCF of Numerators as per given numbers 864/12, 522/7562 is

GCF of Numerators i.e. for 864,522 is 18

LCM of denominators i.e. for 12,7562 is 45372.

Thus, GCF of Fractions is 18/45372.Finally, GCF of Fractions for 864/12, 522/7562 is 18/45372.