How to Find GCF of 400/470, 5832/4796?

GCF of 400/470, 5832/4796

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 400/470, 5832/4796 i.e 8/1127060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 400/470, 5832/4796.

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 400/470,5832/4796?

Given fractions are 400/470,5832/4796

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 400/470,5832/4796, numerators are 400,5832

Denominators are 470,4796

The GCF of 400,5832 is 8 .

LCM of 470,4796 is 1127060.

The greatest common factor of 400/470,5832/4796 = [GCF of 400,5832]/[LCM of 470,4796]= 8/1127060

Therefore, the GCF of 400/470,5832/4796 is 8/1127060.

Greatest Common Factor of 400,5832

To find the highest common factor of 400,5832, we have to find the factors of both numbers and list the highest common factor.

The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

The factors of 5832 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 729, 972, 1458, 1944, 2916, 5832

The HCF of 400,5832 is 8.

Lets's calculate GCF of 400,5832

Greatest Common Factor (GCF) of 400,5832 By Common Division

2	400, 5832
2	200, 2916
2	100, 1458
	50, 729

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 400,5832 By Matching Biggest Common Factor Method

Now, list down the factors of 400

1,2,4,5,8,10,16,20,25,40,50,80,100,200,400

Now, list down the factors of 5832

1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,243,324,486,648,729,972,1458,1944,2916,5832

Greatest Common Factor

We found the factors 400,5832 . The biggest common factor number is the GCF number.
So the greatest common factor 400,5832 is 8.

Lets's calculate LCM of 470,4796

Lowest Common Multiple of 470,4796 using Common Division

2	470, 4796
	235, 2398

∴ So the LCM of the given numbers is 2 x 235 x 2398 = 1127060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/1127060

Therefore, the GCF of Fractions 400/470,5832/4796 is 8/1127060

Least Common Multiple of 470,4796 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 470,4796 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(470,4796) = 2

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

GCF(470,4796) x common factors =2 x 1 = 2

LCM(470,4796) = ( 470 × 4796 ) / 2

LCM(470,4796) = 2254120 / 2

LCM(470,4796) = 1127060

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FAQs on GCF of Fractions of 400/470, 5832/4796

1. What is the HCF of 400,5832?

The HCF of 400,5832 is 8

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 400/470, 5832/4796?

Answer: GCF of Numerators as per given numbers 400/470, 5832/4796 is

GCF of Numerators i.e. for 400,5832 is 8

LCM of denominators i.e. for 470,4796 is 1127060.

Thus, GCF of Fractions is 8/1127060.Finally, GCF of Fractions for 400/470, 5832/4796 is 8/1127060.