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GCF of 975/72, 406/471

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 975/72, 406/471 i.e 1/11304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 975/72, 406/471.

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 975/72,406/471?

Given fractions are 975/72,406/471

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 975/72,406/471, numerators are 975,406

Denominators are 72,471

The GCF of 975,406 is 1 .

LCM of 72,471 is 11304.

The greatest common factor of 975/72,406/471 = [GCF of 975,406]/[LCM of 72,471]= 1/11304

Therefore, the GCF of 975/72,406/471 is 1/11304.

Greatest Common Factor of 975,406

To find the highest common factor of 975,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975

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

The HCF of 975,406 is 1.

Lets's calculate GCF of 975,406

Greatest Common Factor (GCF) of 975,406 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 975,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 975,406 By Matching Biggest Common Factor Method

Now, list down the factors of 975

:

1,3,5,13,15,25,39,65,75,195,325,975

Now, list down the factors of 406

:

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

Greatest Common Factor

We found the factors 975,406 . The biggest common factor number is the GCF number.
So the greatest common factor 975,406 is 1.

Lets's calculate LCM of 72,471

Lowest Common Multiple of 72,471 using Common Division

3 72, 471
24, 157

∴ So the LCM of the given numbers is 3 x 24 x 157 = 11304

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11304

Therefore, the GCF of Fractions 975/72,406/471 is 1/11304

Least Common Multiple of 72,471 with GCF Formula

Least Common Multiple of 72,471 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 72,471 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(72,471) = 3

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

GCF(72,471) x common factors =3 x 1 = 3

LCM(72,471) = ( 72 × 471 ) / 3

LCM(72,471) = 33912 / 3

LCM(72,471) = 11304


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FAQs on GCF of Fractions of 975/72, 406/471

1. What is the HCF of 975,406?

The HCF of 975,406 is 1

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 975/72, 406/471?

Answer: GCF of Numerators as per given numbers 975/72, 406/471 is

GCF of Numerators i.e. for 975,406 is 1

LCM of denominators i.e. for 72,471 is 11304.

Thus, GCF of Fractions is 1/11304.Finally, GCF of Fractions for 975/72, 406/471 is 1/11304.