**Prime factorization** is a way of expressing a number as a product of its **prime factors**. A **prime** number is a number that has exactly two **factors**, 1 and the number itself. **Factor** is a number that divides another number evenly i.e., with no
remainder.

Question:

A **factor tree** is a diagram used to determine the prime **factors** of a natural number greater
than one.

1.
Divide 36
by 2

36 / 2 = 18

quotient
* divisor = dividend

18 * 2 = 36

2.
Write 36
as12 * 2 in the factor tree. 2 is a prime number so divide 18 by 2 = 9

3.
Write 12
as 2 * 9 in the factor tree. 2 is a prime number so divide 9 by 2. 9 cannot be
evenly divided by 2 so divide 9 by 3 = 3.

4. Write 6 as 3 * 3 in the factor tree. 3 and 3 are prime factors so it is fully factorized.

5.
An **index** number is a number which is raised to a power.

e.g. m * m * m *
m* m = m^{5}

6.
36 = 2 * 2 * 3 * 3

36 = 2^{2}
* 3^{2}