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GCF of 174/55, 406/412

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 174/55, 406/412 i.e 58/22660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 174/55, 406/412.

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 174/55,406/412?

Given fractions are 174/55,406/412

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 174/55,406/412, numerators are 174,406

Denominators are 55,412

The GCF of 174,406 is 58 .

LCM of 55,412 is 22660.

The greatest common factor of 174/55,406/412 = [GCF of 174,406]/[LCM of 55,412]= 58/22660

Therefore, the GCF of 174/55,406/412 is 58/22660.

Greatest Common Factor of 174,406

To find the highest common factor of 174,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174

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

The HCF of 174,406 is 58.

Lets's calculate GCF of 174,406

Greatest Common Factor (GCF) of 174,406 By Common Division

2 174, 406
29 87, 203
3, 7

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

Greatest Common Factor of 174,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 174,406 By Matching Biggest Common Factor Method

Now, list down the factors of 174

:

1,2,3,6,29,58,87,174

Now, list down the factors of 406

:

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

Greatest Common Factor

We found the factors 174,406 . The biggest common factor number is the GCF number.
So the greatest common factor 174,406 is 58.

Lets's calculate LCM of 55,412

Lowest Common Multiple of 55,412 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 22660

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 58/22660

Therefore, the GCF of Fractions 174/55,406/412 is 58/22660

Least Common Multiple of 55,412 with GCF Formula

Least Common Multiple of 55,412 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 55,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(55,412) = 1

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

GCF(55,412) x common factors =1 x 1 = 1

LCM(55,412) = ( 55 × 412 ) / 1

LCM(55,412) = 22660 / 1

LCM(55,412) = 22660


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FAQs on GCF of Fractions of 174/55, 406/412

1. What is the HCF of 174,406?

The HCF of 174,406 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 174/55, 406/412?

Answer: GCF of Numerators as per given numbers 174/55, 406/412 is

GCF of Numerators i.e. for 174,406 is 58

LCM of denominators i.e. for 55,412 is 22660.

Thus, GCF of Fractions is 58/22660.Finally, GCF of Fractions for 174/55, 406/412 is 58/22660.