Factors of a number refer to the numbers that can be multiplied together to give the original number as a product. In this case, we will be looking at the factors of 21.

To find the factors of 21, we need to identify all the numbers that divide 21 exactly without leaving any remainder.

## Factors of 21

**Step 1**

List the first few numbers that can divide 21 without leaving a remainder. These numbers are 1, 3, 7, and 21.

**Step 2**

Check if any other numbers can divide 21 exactly. We can do this by dividing 21 by other numbers to see if there is any remainder.

- For instance, dividing 21 by 2 gives a remainder of 1.
- Dividing 21 by 4 gives a remainder of 1.
- Dividing 21 by 5 gives a remainder of 1.
- Dividing 21 by 6 gives a remainder of 3.
- Dividing 21 by 8 gives a remainder of 5
- Dividing 21 by 9 gives a remainder of 3.
- Dividing 21 by 10 gives a remainder of 1.
- Dividing 21 by 11 gives a remainder of 10.
- Dividing 21 by 12 gives a remainder of 9.
- Dividing 21 by 13 gives a remainder of 8.
- Dividing 21 by 14 gives no remainder, but we already have 7 as a factor.

**Step 3**

Write down all the factors of 21. From the above steps, we can see that the factors of 21 are 1, 3, 7, and 21.

**Therefore, the factors of 21 are 1, 3, 7, and 21.**

## Simplifying expressions with exponents

Simplifying expressions with exponents is a crucial concept in mathematics. The rules for simplifying expressions with exponents depend on the type of operation being performed. In this case, we will be looking at simplifying expressions with exponents that involve multiplication.

**Example: Simplify (2^3)(2^5)**

**Step 1**

Recall that when multiplying numbers with the same base, we add the exponents. In this case, the base is 2.

**Step 2**

Add the exponents to simplify the expression.

(2^3)(2^5) = 2^(3+5) = 2^8

**Therefore, (2^3)(2^5) simplifies to 2^8.**

## Solving equations with fractions

Solving equations with fractions can be challenging, but the key is to isolate the variable by performing inverse operations. Inverse operations are operations that undo each other. For example, addition and subtraction are inverse operations, and multiplication and division are inverse operations.

**Example: Solve for x: (3/4)x + 5 = 11**

**Step 1**

Subtract 5 from both sides of the equation to isolate the variable.

(3/4)x = 6

**Step 2**

Multiply both sides of the equation by the reciprocal of 3/4, which is 4/3. This will cancel out the fraction on the left-hand side of the equation.

(4/3)(3/4)x = (4/3)(6)

x = 8

**Therefore, the solution to the equation (3/4)x + 5 = 11 is x = 8.**

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