How to Find GCF of 432/21, 744/440?

GCF of 432/21, 744/440

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 432/21, 744/440 i.e 24/9240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 432/21, 744/440.

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 432/21,744/440?

Given fractions are 432/21,744/440

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 432/21,744/440, numerators are 432,744

Denominators are 21,440

The GCF of 432,744 is 24 .

LCM of 21,440 is 9240.

The greatest common factor of 432/21,744/440 = [GCF of 432,744]/[LCM of 21,440]= 24/9240

Therefore, the GCF of 432/21,744/440 is 24/9240.

Greatest Common Factor of 432,744

To find the highest common factor of 432,744, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 744 are 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744

The HCF of 432,744 is 24.

Lets's calculate GCF of 432,744

Greatest Common Factor (GCF) of 432,744 By Common Division

2	432, 744
2	216, 372
2	108, 186
3	54, 93
	18, 31

∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24

Greatest Common Factor of 432,744 By Matching Biggest Common Factor Method

Now, list down the factors of 432

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

Now, list down the factors of 744

1,2,3,4,6,8,12,24,31,62,93,124,186,248,372,744

Greatest Common Factor

We found the factors 432,744 . The biggest common factor number is the GCF number.
So the greatest common factor 432,744 is 24.

Lets's calculate LCM of 21,440

Lowest Common Multiple of 21,440 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9240

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/9240

Therefore, the GCF of Fractions 432/21,744/440 is 24/9240

Least Common Multiple of 21,440 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 21,440 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,440) = 1

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

GCF(21,440) x common factors =1 x 1 = 1

LCM(21,440) = ( 21 × 440 ) / 1

LCM(21,440) = 9240 / 1

LCM(21,440) = 9240

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FAQs on GCF of Fractions of 432/21, 744/440

1. What is the HCF of 432,744?

The HCF of 432,744 is 24

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 432/21, 744/440?

Answer: GCF of Numerators as per given numbers 432/21, 744/440 is

GCF of Numerators i.e. for 432,744 is 24

LCM of denominators i.e. for 21,440 is 9240.

Thus, GCF of Fractions is 24/9240.Finally, GCF of Fractions for 432/21, 744/440 is 24/9240.