How to Find GCF of 199/164, 648/644?

GCF of 199/164, 648/644

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 199/164, 648/644 i.e 1/26404 easily. The following is the detailed procedure to determine the greatest common factor of fractions 199/164, 648/644.

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 199/164,648/644?

Given fractions are 199/164,648/644

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 199/164,648/644, numerators are 199,648

Denominators are 164,644

The GCF of 199,648 is 1 .

LCM of 164,644 is 26404.

The greatest common factor of 199/164,648/644 = [GCF of 199,648]/[LCM of 164,644]= 1/26404

Therefore, the GCF of 199/164,648/644 is 1/26404.

Greatest Common Factor of 199,648

To find the highest common factor of 199,648, we have to find the factors of both numbers and list the highest common factor.

The factors of 199 are 1, 199

The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648

The HCF of 199,648 is 1.

Lets's calculate GCF of 199,648

Greatest Common Factor (GCF) of 199,648 By Common Division

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

Greatest Common Factor of 199,648 By Matching Biggest Common Factor Method

Now, list down the factors of 199

1,199

Now, list down the factors of 648

1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,324,648

Greatest Common Factor

We found the factors 199,648 . The biggest common factor number is the GCF number.
So the greatest common factor 199,648 is 1.

Lets's calculate LCM of 164,644

Lowest Common Multiple of 164,644 using Common Division

2	164, 644
2	82, 322
	41, 161

∴ So the LCM of the given numbers is 2 x 2 x 41 x 161 = 26404

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26404

Therefore, the GCF of Fractions 199/164,648/644 is 1/26404

Least Common Multiple of 164,644 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 164,644 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(164,644) = 4

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

GCF(164,644) x common factors =4 x 1 = 4

LCM(164,644) = ( 164 × 644 ) / 4

LCM(164,644) = 105616 / 4

LCM(164,644) = 26404

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FAQs on GCF of Fractions of 199/164, 648/644

1. What is the HCF of 199,648?

The HCF of 199,648 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 199/164, 648/644?

Answer: GCF of Numerators as per given numbers 199/164, 648/644 is

GCF of Numerators i.e. for 199,648 is 1

LCM of denominators i.e. for 164,644 is 26404.

Thus, GCF of Fractions is 1/26404.Finally, GCF of Fractions for 199/164, 648/644 is 1/26404.