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GCF of 270/345, 326/406

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 270/345, 326/406 i.e 2/140070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 270/345, 326/406.

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 270/345,326/406?

Given fractions are 270/345,326/406

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 270/345,326/406, numerators are 270,326

Denominators are 345,406

The GCF of 270,326 is 2 .

LCM of 345,406 is 140070.

The greatest common factor of 270/345,326/406 = [GCF of 270,326]/[LCM of 345,406]= 2/140070

Therefore, the GCF of 270/345,326/406 is 2/140070.

Greatest Common Factor of 270,326

To find the highest common factor of 270,326, we have to find the factors of both numbers and list the highest common factor.

The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270

The factors of 326 are 1, 2, 163, 326

The HCF of 270,326 is 2.

Lets's calculate GCF of 270,326

Greatest Common Factor (GCF) of 270,326 By Common Division

2 270, 326
135, 163

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

Greatest Common Factor of 270,326 By Matching Biggest Common Factor Method

Greatest Common Factor of 270,326 By Matching Biggest Common Factor Method

Now, list down the factors of 270

:

1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270

Now, list down the factors of 326

:

1,2,163,326

Greatest Common Factor

We found the factors 270,326 . The biggest common factor number is the GCF number.
So the greatest common factor 270,326 is 2.

Lets's calculate LCM of 345,406

Lowest Common Multiple of 345,406 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 140070

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/140070

Therefore, the GCF of Fractions 270/345,326/406 is 2/140070

Least Common Multiple of 345,406 with GCF Formula

Least Common Multiple of 345,406 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 345,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(345,406) = 1

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

GCF(345,406) x common factors =1 x 1 = 1

LCM(345,406) = ( 345 × 406 ) / 1

LCM(345,406) = 140070 / 1

LCM(345,406) = 140070


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FAQs on GCF of Fractions of 270/345, 326/406

1. What is the HCF of 270,326?

The HCF of 270,326 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 270/345, 326/406?

Answer: GCF of Numerators as per given numbers 270/345, 326/406 is

GCF of Numerators i.e. for 270,326 is 2

LCM of denominators i.e. for 345,406 is 140070.

Thus, GCF of Fractions is 2/140070.Finally, GCF of Fractions for 270/345, 326/406 is 2/140070.