How to Find GCF of 864/224, 108/641?

GCF of 864/224, 108/641

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 864/224, 108/641 i.e 108/143584 easily. The following is the detailed procedure to determine the greatest common factor of fractions 864/224, 108/641.

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 864/224,108/641?

Given fractions are 864/224,108/641

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 864/224,108/641, numerators are 864,108

Denominators are 224,641

The GCF of 864,108 is 108 .

LCM of 224,641 is 143584.

The greatest common factor of 864/224,108/641 = [GCF of 864,108]/[LCM of 224,641]= 108/143584

Therefore, the GCF of 864/224,108/641 is 108/143584.

Greatest Common Factor of 864,108

To find the highest common factor of 864,108, 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 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The HCF of 864,108 is 108.

Lets's calculate GCF of 864,108

Greatest Common Factor (GCF) of 864,108 By Common Division

2	864, 108
2	432, 54
3	216, 27
3	72, 9
3	24, 3
	8, 1

∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 x 3 = 108

Greatest Common Factor of 864,108 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 108

1,2,3,4,6,9,12,18,27,36,54,108

Greatest Common Factor

We found the factors 864,108 . The biggest common factor number is the GCF number.
So the greatest common factor 864,108 is 108.

Lets's calculate LCM of 224,641

Lowest Common Multiple of 224,641 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 143584

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 108/143584

Therefore, the GCF of Fractions 864/224,108/641 is 108/143584

Least Common Multiple of 224,641 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 224,641 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(224,641) = 1

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

GCF(224,641) x common factors =1 x 1 = 1

LCM(224,641) = ( 224 × 641 ) / 1

LCM(224,641) = 143584 / 1

LCM(224,641) = 143584

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FAQs on GCF of Fractions of 864/224, 108/641

1. What is the HCF of 864,108?

The HCF of 864,108 is 108

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 864/224, 108/641?

Answer: GCF of Numerators as per given numbers 864/224, 108/641 is

GCF of Numerators i.e. for 864,108 is 108

LCM of denominators i.e. for 224,641 is 143584.

Thus, GCF of Fractions is 108/143584.Finally, GCF of Fractions for 864/224, 108/641 is 108/143584.