How to Find GCF of 424/409, 9664/575?

GCF of 424/409, 9664/575

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 424/409, 9664/575 i.e 8/235175 easily. The following is the detailed procedure to determine the greatest common factor of fractions 424/409, 9664/575.

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 424/409,9664/575?

Given fractions are 424/409,9664/575

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 424/409,9664/575, numerators are 424,9664

Denominators are 409,575

The GCF of 424,9664 is 8 .

LCM of 409,575 is 235175.

The greatest common factor of 424/409,9664/575 = [GCF of 424,9664]/[LCM of 409,575]= 8/235175

Therefore, the GCF of 424/409,9664/575 is 8/235175.

Greatest Common Factor of 424,9664

To find the highest common factor of 424,9664, we have to find the factors of both numbers and list the highest common factor.

The factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424

The factors of 9664 are 1, 2, 4, 8, 16, 32, 64, 151, 302, 604, 1208, 2416, 4832, 9664

The HCF of 424,9664 is 8.

Lets's calculate GCF of 424,9664

Greatest Common Factor (GCF) of 424,9664 By Common Division

2	424, 9664
2	212, 4832
2	106, 2416
	53, 1208

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

Greatest Common Factor of 424,9664 By Matching Biggest Common Factor Method

Now, list down the factors of 424

1,2,4,8,53,106,212,424

Now, list down the factors of 9664

1,2,4,8,16,32,64,151,302,604,1208,2416,4832,9664

Greatest Common Factor

We found the factors 424,9664 . The biggest common factor number is the GCF number.
So the greatest common factor 424,9664 is 8.

Lets's calculate LCM of 409,575

Lowest Common Multiple of 409,575 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 235175

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/235175

Therefore, the GCF of Fractions 424/409,9664/575 is 8/235175

Least Common Multiple of 409,575 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 409,575 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(409,575) = 1

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

GCF(409,575) x common factors =1 x 1 = 1

LCM(409,575) = ( 409 × 575 ) / 1

LCM(409,575) = 235175 / 1

LCM(409,575) = 235175

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FAQs on GCF of Fractions of 424/409, 9664/575

1. What is the HCF of 424,9664?

The HCF of 424,9664 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 424/409, 9664/575?

Answer: GCF of Numerators as per given numbers 424/409, 9664/575 is

GCF of Numerators i.e. for 424,9664 is 8

LCM of denominators i.e. for 409,575 is 235175.

Thus, GCF of Fractions is 8/235175.Finally, GCF of Fractions for 424/409, 9664/575 is 8/235175.