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GCF of 490/85, 406/8180

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 490/85, 406/8180 i.e 14/139060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 490/85, 406/8180.

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 490/85,406/8180?

Given fractions are 490/85,406/8180

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 490/85,406/8180, numerators are 490,406

Denominators are 85,8180

The GCF of 490,406 is 14 .

LCM of 85,8180 is 139060.

The greatest common factor of 490/85,406/8180 = [GCF of 490,406]/[LCM of 85,8180]= 14/139060

Therefore, the GCF of 490/85,406/8180 is 14/139060.

Greatest Common Factor of 490,406

To find the highest common factor of 490,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 490,406 is 14.

Lets's calculate GCF of 490,406

Greatest Common Factor (GCF) of 490,406 By Common Division

2 490, 406
7 245, 203
35, 29

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 490,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 490,406 By Matching Biggest Common Factor Method

Now, list down the factors of 490

:

1,2,5,7,10,14,35,49,70,98,245,490

Now, list down the factors of 406

:

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 490,406 . The biggest common factor number is the GCF number.
So the greatest common factor 490,406 is 14.

Lets's calculate LCM of 85,8180

Lowest Common Multiple of 85,8180 using Common Division

5 85, 8180
17, 1636

∴ So the LCM of the given numbers is 5 x 17 x 1636 = 139060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/139060

Therefore, the GCF of Fractions 490/85,406/8180 is 14/139060

Least Common Multiple of 85,8180 with GCF Formula

Least Common Multiple of 85,8180 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 85,8180 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(85,8180) = 5

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

GCF(85,8180) x common factors =5 x 1 = 5

LCM(85,8180) = ( 85 × 8180 ) / 5

LCM(85,8180) = 695300 / 5

LCM(85,8180) = 139060


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FAQs on GCF of Fractions of 490/85, 406/8180

1. What is the HCF of 490,406?

The HCF of 490,406 is 14

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 490/85, 406/8180?

Answer: GCF of Numerators as per given numbers 490/85, 406/8180 is

GCF of Numerators i.e. for 490,406 is 14

LCM of denominators i.e. for 85,8180 is 139060.

Thus, GCF of Fractions is 14/139060.Finally, GCF of Fractions for 490/85, 406/8180 is 14/139060.