How to Find GCF of 408/259, 544/960?

GCF of 408/259, 544/960

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 408/259, 544/960 i.e 136/248640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/259, 544/960.

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 408/259,544/960?

Given fractions are 408/259,544/960

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 408/259,544/960, numerators are 408,544

Denominators are 259,960

The GCF of 408,544 is 136 .

LCM of 259,960 is 248640.

The greatest common factor of 408/259,544/960 = [GCF of 408,544]/[LCM of 259,960]= 136/248640

Therefore, the GCF of 408/259,544/960 is 136/248640.

Greatest Common Factor of 408,544

To find the highest common factor of 408,544, we have to find the factors of both numbers and list the highest common factor.

The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408

The factors of 544 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544

The HCF of 408,544 is 136.

Lets's calculate GCF of 408,544

Greatest Common Factor (GCF) of 408,544 By Common Division

2	408, 544
2	204, 272
2	102, 136
17	51, 68
	3, 4

∴ So the GCF of the given numbers is 2 x 2 x 2 x 17 = 136

Greatest Common Factor of 408,544 By Matching Biggest Common Factor Method

Now, list down the factors of 408

1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408

Now, list down the factors of 544

1,2,4,8,16,17,32,34,68,136,272,544

Greatest Common Factor

We found the factors 408,544 . The biggest common factor number is the GCF number.
So the greatest common factor 408,544 is 136.

Lets's calculate LCM of 259,960

Lowest Common Multiple of 259,960 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 248640

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 136/248640

Therefore, the GCF of Fractions 408/259,544/960 is 136/248640

Least Common Multiple of 259,960 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 259,960 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(259,960) = 1

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

GCF(259,960) x common factors =1 x 1 = 1

LCM(259,960) = ( 259 × 960 ) / 1

LCM(259,960) = 248640 / 1

LCM(259,960) = 248640

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FAQs on GCF of Fractions of 408/259, 544/960

1. What is the HCF of 408,544?

The HCF of 408,544 is 136

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 408/259, 544/960?

Answer: GCF of Numerators as per given numbers 408/259, 544/960 is

GCF of Numerators i.e. for 408,544 is 136

LCM of denominators i.e. for 259,960 is 248640.

Thus, GCF of Fractions is 136/248640.Finally, GCF of Fractions for 408/259, 544/960 is 136/248640.