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GCF of 406/65, 574/317

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 406/65, 574/317 i.e 14/20605 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/65, 574/317.

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 406/65,574/317?

Given fractions are 406/65,574/317

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 406/65,574/317, numerators are 406,574

Denominators are 65,317

The GCF of 406,574 is 14 .

LCM of 65,317 is 20605.

The greatest common factor of 406/65,574/317 = [GCF of 406,574]/[LCM of 65,317]= 14/20605

Therefore, the GCF of 406/65,574/317 is 14/20605.

Greatest Common Factor of 406,574

To find the highest common factor of 406,574, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574

The HCF of 406,574 is 14.

Lets's calculate GCF of 406,574

Greatest Common Factor (GCF) of 406,574 By Common Division

2 406, 574
7 203, 287
29, 41

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

Greatest Common Factor of 406,574 By Matching Biggest Common Factor Method

Greatest Common Factor of 406,574 By Matching Biggest Common Factor Method

Now, list down the factors of 406

:

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

Now, list down the factors of 574

:

1,2,7,14,41,82,287,574

Greatest Common Factor

We found the factors 406,574 . The biggest common factor number is the GCF number.
So the greatest common factor 406,574 is 14.

Lets's calculate LCM of 65,317

Lowest Common Multiple of 65,317 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 20605

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/20605

Therefore, the GCF of Fractions 406/65,574/317 is 14/20605

Least Common Multiple of 65,317 with GCF Formula

Least Common Multiple of 65,317 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 65,317 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,317) = 1

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

GCF(65,317) x common factors =1 x 1 = 1

LCM(65,317) = ( 65 × 317 ) / 1

LCM(65,317) = 20605 / 1

LCM(65,317) = 20605


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FAQs on GCF of Fractions of 406/65, 574/317

1. What is the HCF of 406,574?

The HCF of 406,574 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 406/65, 574/317?

Answer: GCF of Numerators as per given numbers 406/65, 574/317 is

GCF of Numerators i.e. for 406,574 is 14

LCM of denominators i.e. for 65,317 is 20605.

Thus, GCF of Fractions is 14/20605.Finally, GCF of Fractions for 406/65, 574/317 is 14/20605.