Finite Math Examples

6 x^{3} + 27.08 x^{2} + 104.4954 x + 1.83

$6 x^{3} + 27.08 x^{2} + 104.4954 x + 1.83$

Step 1

Since

6 x^{3}, 27.08 x^{2}, 104.4954 x, 1.83

$6 x^{3}, 27.08 x^{2}, 104.4954 x, 1.83$ contains both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part, then find GCF for the variable part.

Steps to find the GCF for

6 x^{3}, 27.08 x^{2}, 104.4954 x, 1.83

$6 x^{3}, 27.08 x^{2}, 104.4954 x, 1.83$ :

1. Find the GCF for the numerical part

6, 27.08, 104.4954, 1.83

$6, 27.08, 104.4954, 1.83$

2. Find the GCF for the variable part

x^{3}, x^{2}, x^{1}

$x^{3}, x^{2}, x^{1}$

3. Multiply the values together

Step 2

Find the common factors for the numerical part:

6, 27.08, 104.4954, 1.83

$6, 27.08, 104.4954, 1.83$

Step 3

The factors for

6

$6$ are

1, 2, 3, 6

$1, 2, 3, 6$ .

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Step 3.1

The factors for

6

$6$ are all numbers between

1

$1$ and

6

$6$ , which divide

6

$6$ evenly.

Check numbers between

1

$1$ and

6

$6$

Step 3.2

Find the factor pairs of

6

$6$ where

x \cdot y = 6

$x \cdot y = 6$ .

\begin{array}{c} x & y \\ 1 & 6 \\ 2 & 3 \end{array}

$\begin{array}{c} x & y \\ 1 & 6 \\ 2 & 3 \end{array}$

Step 3.3

List the factors for

6

$6$ .

1, 2, 3, 6

$1, 2, 3, 6$

1, 2, 3, 6

$1, 2, 3, 6$

Step 4

There are no factors for

27.08

$27.08$ .

No factors

Step 5

There are no factors for

104.4954

$104.4954$ .

No factors

Step 6

There are no factors for

1.83

$1.83$ .

No factors

Step 7

List all the factors for

6, 27.08, 104.4954, 1.83

$6, 27.08, 104.4954, 1.83$ to find the common factors.

6

$6$ :

1, 2, 3, 6

$1, 2, 3, 6$

27.08

$27.08$ : No factors

104.4954

$104.4954$ : No factors

1.83

$1.83$ : No factors

Step 8

The common factors for

6, 27.08, 104.4954, 1.83

$6, 27.08, 104.4954, 1.83$ are

Step 9

The numbers do not contain any common variable factors. The GCF (HCF) of the numerical factors

\frac{1 \cdot 1.83}{183}

$\frac{1 \cdot 1.83}{183}$ .

\frac{1 \cdot 1.83}{183}

$\frac{1 \cdot 1.83}{183}$