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GCF of 470/490, 442/223

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 470/490, 442/223 i.e 2/109270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 470/490, 442/223.

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 470/490,442/223?

Given fractions are 470/490,442/223

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 470/490,442/223, numerators are 470,442

Denominators are 490,223

The GCF of 470,442 is 2 .

LCM of 490,223 is 109270.

The greatest common factor of 470/490,442/223 = [GCF of 470,442]/[LCM of 490,223]= 2/109270

Therefore, the GCF of 470/490,442/223 is 2/109270.

Greatest Common Factor of 470,442

To find the highest common factor of 470,442, we have to find the factors of both numbers and list the highest common factor.

The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470

The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442

The HCF of 470,442 is 2.

Lets's calculate GCF of 470,442

Greatest Common Factor (GCF) of 470,442 By Common Division

2 470, 442
235, 221

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

Greatest Common Factor of 470,442 By Matching Biggest Common Factor Method

Greatest Common Factor of 470,442 By Matching Biggest Common Factor Method

Now, list down the factors of 470

:

1,2,5,10,47,94,235,470

Now, list down the factors of 442

:

1,2,13,17,26,34,221,442

Greatest Common Factor

We found the factors 470,442 . The biggest common factor number is the GCF number.
So the greatest common factor 470,442 is 2.

Lets's calculate LCM of 490,223

Lowest Common Multiple of 490,223 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 109270

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/109270

Therefore, the GCF of Fractions 470/490,442/223 is 2/109270

Least Common Multiple of 490,223 with GCF Formula

Least Common Multiple of 490,223 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 490,223 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(490,223) = 1

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

GCF(490,223) x common factors =1 x 1 = 1

LCM(490,223) = ( 490 × 223 ) / 1

LCM(490,223) = 109270 / 1

LCM(490,223) = 109270


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FAQs on GCF of Fractions of 470/490, 442/223

1. What is the HCF of 470,442?

The HCF of 470,442 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 470/490, 442/223?

Answer: GCF of Numerators as per given numbers 470/490, 442/223 is

GCF of Numerators i.e. for 470,442 is 2

LCM of denominators i.e. for 490,223 is 109270.

Thus, GCF of Fractions is 2/109270.Finally, GCF of Fractions for 470/490, 442/223 is 2/109270.