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GCF of 401/65, 814/512

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 401/65, 814/512 i.e 1/33280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 401/65, 814/512.

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 401/65,814/512?

Given fractions are 401/65,814/512

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 401/65,814/512, numerators are 401,814

Denominators are 65,512

The GCF of 401,814 is 1 .

LCM of 65,512 is 33280.

The greatest common factor of 401/65,814/512 = [GCF of 401,814]/[LCM of 65,512]= 1/33280

Therefore, the GCF of 401/65,814/512 is 1/33280.

Greatest Common Factor of 401,814

To find the highest common factor of 401,814, we have to find the factors of both numbers and list the highest common factor.

The factors of 401 are 1, 401

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

The HCF of 401,814 is 1.

Lets's calculate GCF of 401,814

Greatest Common Factor (GCF) of 401,814 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 401,814 By Matching Biggest Common Factor Method

Greatest Common Factor of 401,814 By Matching Biggest Common Factor Method

Now, list down the factors of 401

:

1,401

Now, list down the factors of 814

:

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

Greatest Common Factor

We found the factors 401,814 . The biggest common factor number is the GCF number.
So the greatest common factor 401,814 is 1.

Lets's calculate LCM of 65,512

Lowest Common Multiple of 65,512 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 33280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/33280

Therefore, the GCF of Fractions 401/65,814/512 is 1/33280

Least Common Multiple of 65,512 with GCF Formula

Least Common Multiple of 65,512 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 65,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,512) = 1

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

GCF(65,512) x common factors =1 x 1 = 1

LCM(65,512) = ( 65 × 512 ) / 1

LCM(65,512) = 33280 / 1

LCM(65,512) = 33280


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FAQs on GCF of Fractions of 401/65, 814/512

1. What is the HCF of 401,814?

The HCF of 401,814 is 1

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 401/65, 814/512?

Answer: GCF of Numerators as per given numbers 401/65, 814/512 is

GCF of Numerators i.e. for 401,814 is 1

LCM of denominators i.e. for 65,512 is 33280.

Thus, GCF of Fractions is 1/33280.Finally, GCF of Fractions for 401/65, 814/512 is 1/33280.