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GCF of 644/76, 814/469

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 644/76, 814/469 i.e 2/35644 easily. The following is the detailed procedure to determine the greatest common factor of fractions 644/76, 814/469.

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 644/76,814/469?

Given fractions are 644/76,814/469

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 644/76,814/469, numerators are 644,814

Denominators are 76,469

The GCF of 644,814 is 2 .

LCM of 76,469 is 35644.

The greatest common factor of 644/76,814/469 = [GCF of 644,814]/[LCM of 76,469]= 2/35644

Therefore, the GCF of 644/76,814/469 is 2/35644.

Greatest Common Factor of 644,814

To find the highest common factor of 644,814, we have to find the factors of both numbers and list the highest common factor.

The factors of 644 are 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644

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

The HCF of 644,814 is 2.

Lets's calculate GCF of 644,814

Greatest Common Factor (GCF) of 644,814 By Common Division

2 644, 814
322, 407

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

Greatest Common Factor of 644,814 By Matching Biggest Common Factor Method

Greatest Common Factor of 644,814 By Matching Biggest Common Factor Method

Now, list down the factors of 644

:

1,2,4,7,14,23,28,46,92,161,322,644

Now, list down the factors of 814

:

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

Greatest Common Factor

We found the factors 644,814 . The biggest common factor number is the GCF number.
So the greatest common factor 644,814 is 2.

Lets's calculate LCM of 76,469

Lowest Common Multiple of 76,469 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 35644

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/35644

Therefore, the GCF of Fractions 644/76,814/469 is 2/35644

Least Common Multiple of 76,469 with GCF Formula

Least Common Multiple of 76,469 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 76,469 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,469) = 1

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

GCF(76,469) x common factors =1 x 1 = 1

LCM(76,469) = ( 76 × 469 ) / 1

LCM(76,469) = 35644 / 1

LCM(76,469) = 35644


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FAQs on GCF of Fractions of 644/76, 814/469

1. What is the HCF of 644,814?

The HCF of 644,814 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 644/76, 814/469?

Answer: GCF of Numerators as per given numbers 644/76, 814/469 is

GCF of Numerators i.e. for 644,814 is 2

LCM of denominators i.e. for 76,469 is 35644.

Thus, GCF of Fractions is 2/35644.Finally, GCF of Fractions for 644/76, 814/469 is 2/35644.