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GCF of 403/23, 208/392

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 403/23, 208/392 i.e 13/9016 easily. The following is the detailed procedure to determine the greatest common factor of fractions 403/23, 208/392.

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 403/23,208/392?

Given fractions are 403/23,208/392

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 403/23,208/392, numerators are 403,208

Denominators are 23,392

The GCF of 403,208 is 13 .

LCM of 23,392 is 9016.

The greatest common factor of 403/23,208/392 = [GCF of 403,208]/[LCM of 23,392]= 13/9016

Therefore, the GCF of 403/23,208/392 is 13/9016.

Greatest Common Factor of 403,208

To find the highest common factor of 403,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 403 are 1, 13, 31, 403

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 403,208 is 13.

Lets's calculate GCF of 403,208

Greatest Common Factor (GCF) of 403,208 By Common Division

13 403, 208
31, 16

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 403,208 By Matching Biggest Common Factor Method

Greatest Common Factor of 403,208 By Matching Biggest Common Factor Method

Now, list down the factors of 403

:

1,13,31,403

Now, list down the factors of 208

:

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 403,208 . The biggest common factor number is the GCF number.
So the greatest common factor 403,208 is 13.

Lets's calculate LCM of 23,392

Lowest Common Multiple of 23,392 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9016

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/9016

Therefore, the GCF of Fractions 403/23,208/392 is 13/9016

Least Common Multiple of 23,392 with GCF Formula

Least Common Multiple of 23,392 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 23,392 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,392) = 1

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

GCF(23,392) x common factors =1 x 1 = 1

LCM(23,392) = ( 23 × 392 ) / 1

LCM(23,392) = 9016 / 1

LCM(23,392) = 9016


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FAQs on GCF of Fractions of 403/23, 208/392

1. What is the HCF of 403,208?

The HCF of 403,208 is 13

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 403/23, 208/392?

Answer: GCF of Numerators as per given numbers 403/23, 208/392 is

GCF of Numerators i.e. for 403,208 is 13

LCM of denominators i.e. for 23,392 is 9016.

Thus, GCF of Fractions is 13/9016.Finally, GCF of Fractions for 403/23, 208/392 is 13/9016.