How to Find GCF of 343/164, 7172/404?

GCF of 343/164, 7172/404

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 343/164, 7172/404 i.e 1/16564 easily. The following is the detailed procedure to determine the greatest common factor of fractions 343/164, 7172/404.

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 343/164,7172/404?

Given fractions are 343/164,7172/404

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 343/164,7172/404, numerators are 343,7172

Denominators are 164,404

The GCF of 343,7172 is 1 .

LCM of 164,404 is 16564.

The greatest common factor of 343/164,7172/404 = [GCF of 343,7172]/[LCM of 164,404]= 1/16564

Therefore, the GCF of 343/164,7172/404 is 1/16564.

Greatest Common Factor of 343,7172

To find the highest common factor of 343,7172, we have to find the factors of both numbers and list the highest common factor.

The factors of 343 are 1, 7, 49, 343

The factors of 7172 are 1, 2, 4, 11, 22, 44, 163, 326, 652, 1793, 3586, 7172

The HCF of 343,7172 is 1.

Lets's calculate GCF of 343,7172

Greatest Common Factor (GCF) of 343,7172 By Common Division

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

Greatest Common Factor of 343,7172 By Matching Biggest Common Factor Method

Now, list down the factors of 343

1,7,49,343

Now, list down the factors of 7172

1,2,4,11,22,44,163,326,652,1793,3586,7172

Greatest Common Factor

We found the factors 343,7172 . The biggest common factor number is the GCF number.
So the greatest common factor 343,7172 is 1.

Lets's calculate LCM of 164,404

Lowest Common Multiple of 164,404 using Common Division

2	164, 404
2	82, 202
	41, 101

∴ So the LCM of the given numbers is 2 x 2 x 41 x 101 = 16564

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16564

Therefore, the GCF of Fractions 343/164,7172/404 is 1/16564

Least Common Multiple of 164,404 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 164,404 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(164,404) = 4

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

GCF(164,404) x common factors =4 x 1 = 4

LCM(164,404) = ( 164 × 404 ) / 4

LCM(164,404) = 66256 / 4

LCM(164,404) = 16564

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FAQs on GCF of Fractions of 343/164, 7172/404

1. What is the HCF of 343,7172?

The HCF of 343,7172 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 343/164, 7172/404?

Answer: GCF of Numerators as per given numbers 343/164, 7172/404 is

GCF of Numerators i.e. for 343,7172 is 1

LCM of denominators i.e. for 164,404 is 16564.

Thus, GCF of Fractions is 1/16564.Finally, GCF of Fractions for 343/164, 7172/404 is 1/16564.