How to Find GCF of 404/82, 164/207?

GCF of 404/82, 164/207

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 404/82, 164/207 i.e 4/16974 easily. The following is the detailed procedure to determine the greatest common factor of fractions 404/82, 164/207.

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 404/82,164/207?

Given fractions are 404/82,164/207

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 404/82,164/207, numerators are 404,164

Denominators are 82,207

The GCF of 404,164 is 4 .

LCM of 82,207 is 16974.

The greatest common factor of 404/82,164/207 = [GCF of 404,164]/[LCM of 82,207]= 4/16974

Therefore, the GCF of 404/82,164/207 is 4/16974.

Greatest Common Factor of 404,164

To find the highest common factor of 404,164, we have to find the factors of both numbers and list the highest common factor.

The factors of 404 are 1, 2, 4, 101, 202, 404

The factors of 164 are 1, 2, 4, 41, 82, 164

The HCF of 404,164 is 4.

Lets's calculate GCF of 404,164

Greatest Common Factor (GCF) of 404,164 By Common Division

2	404, 164
2	202, 82
	101, 41

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 404,164 By Matching Biggest Common Factor Method

Now, list down the factors of 404

1,2,4,101,202,404

Now, list down the factors of 164

1,2,4,41,82,164

Greatest Common Factor

We found the factors 404,164 . The biggest common factor number is the GCF number.
So the greatest common factor 404,164 is 4.

Lets's calculate LCM of 82,207

Lowest Common Multiple of 82,207 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 16974

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/16974

Therefore, the GCF of Fractions 404/82,164/207 is 4/16974

Least Common Multiple of 82,207 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 82,207 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(82,207) = 1

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

GCF(82,207) x common factors =1 x 1 = 1

LCM(82,207) = ( 82 × 207 ) / 1

LCM(82,207) = 16974 / 1

LCM(82,207) = 16974

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FAQs on GCF of Fractions of 404/82, 164/207

1. What is the HCF of 404,164?

The HCF of 404,164 is 4

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 404/82, 164/207?

Answer: GCF of Numerators as per given numbers 404/82, 164/207 is

GCF of Numerators i.e. for 404,164 is 4

LCM of denominators i.e. for 82,207 is 16974.

Thus, GCF of Fractions is 4/16974.Finally, GCF of Fractions for 404/82, 164/207 is 4/16974.