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GCF of 144/604, 814/256

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 144/604, 814/256 i.e 2/38656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 144/604, 814/256.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 144/604,814/256?

Given fractions are 144/604,814/256

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 144/604,814/256, numerators are 144,814

Denominators are 604,256

The GCF of 144,814 is 2 .

LCM of 604,256 is 38656.

The greatest common factor of 144/604,814/256 = [GCF of 144,814]/[LCM of 604,256]= 2/38656

Therefore, the GCF of 144/604,814/256 is 2/38656.

Greatest Common Factor of 144,814

To find the highest common factor of 144,814, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814

The HCF of 144,814 is 2.

Lets's calculate GCF of 144,814

Greatest Common Factor (GCF) of 144,814 By Common Division

2 144, 814
72, 407

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

Greatest Common Factor of 144,814 By Matching Biggest Common Factor Method

Greatest Common Factor of 144,814 By Matching Biggest Common Factor Method

Now, list down the factors of 144

:

1,2,3,4,6,8,9,12,16,18,24,36,48,72,144

Now, list down the factors of 814

:

1,2,11,22,37,74,407,814

Greatest Common Factor

We found the factors 144,814 . The biggest common factor number is the GCF number.
So the greatest common factor 144,814 is 2.

Lets's calculate LCM of 604,256

Lowest Common Multiple of 604,256 using Common Division

2 604, 256
2 302, 128
151, 64

∴ So the LCM of the given numbers is 2 x 2 x 151 x 64 = 38656

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/38656

Therefore, the GCF of Fractions 144/604,814/256 is 2/38656

Least Common Multiple of 604,256 with GCF Formula

Least Common Multiple of 604,256 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 604,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(604,256) = 4

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

GCF(604,256) x common factors =4 x 1 = 4

LCM(604,256) = ( 604 × 256 ) / 4

LCM(604,256) = 154624 / 4

LCM(604,256) = 38656


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FAQs on GCF of Fractions of 144/604, 814/256

1. What is the HCF of 144,814?

The HCF of 144,814 is 2

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 144/604, 814/256?

Answer: GCF of Numerators as per given numbers 144/604, 814/256 is

GCF of Numerators i.e. for 144,814 is 2

LCM of denominators i.e. for 604,256 is 38656.

Thus, GCF of Fractions is 2/38656.Finally, GCF of Fractions for 144/604, 814/256 is 2/38656.