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GCF of 580/637, 406/180

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 580/637, 406/180 i.e 58/114660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 580/637, 406/180.

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 580/637,406/180?

Given fractions are 580/637,406/180

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 580/637,406/180, numerators are 580,406

Denominators are 637,180

The GCF of 580,406 is 58 .

LCM of 637,180 is 114660.

The greatest common factor of 580/637,406/180 = [GCF of 580,406]/[LCM of 637,180]= 58/114660

Therefore, the GCF of 580/637,406/180 is 58/114660.

Greatest Common Factor of 580,406

To find the highest common factor of 580,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580

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

The HCF of 580,406 is 58.

Lets's calculate GCF of 580,406

Greatest Common Factor (GCF) of 580,406 By Common Division

2 580, 406
29 290, 203
10, 7

∴ So the GCF of the given numbers is 2 x 29 = 58

Greatest Common Factor of 580,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 580,406 By Matching Biggest Common Factor Method

Now, list down the factors of 580

:

1,2,4,5,10,20,29,58,116,145,290,580

Now, list down the factors of 406

:

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

Greatest Common Factor

We found the factors 580,406 . The biggest common factor number is the GCF number.
So the greatest common factor 580,406 is 58.

Lets's calculate LCM of 637,180

Lowest Common Multiple of 637,180 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 114660

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 58/114660

Therefore, the GCF of Fractions 580/637,406/180 is 58/114660

Least Common Multiple of 637,180 with GCF Formula

Least Common Multiple of 637,180 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 637,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(637,180) = 1

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

GCF(637,180) x common factors =1 x 1 = 1

LCM(637,180) = ( 637 × 180 ) / 1

LCM(637,180) = 114660 / 1

LCM(637,180) = 114660


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FAQs on GCF of Fractions of 580/637, 406/180

1. What is the HCF of 580,406?

The HCF of 580,406 is 58

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 580/637, 406/180?

Answer: GCF of Numerators as per given numbers 580/637, 406/180 is

GCF of Numerators i.e. for 580,406 is 58

LCM of denominators i.e. for 637,180 is 114660.

Thus, GCF of Fractions is 58/114660.Finally, GCF of Fractions for 580/637, 406/180 is 58/114660.