Prime Factorization and Exponents Mrs. Rotunno 5 th Grade x 3 x 5 x 5 x 5 = 3² x 5³

Prime Factorization is... A number written as a product of prime factors. 2 X 2 X 2 X 3 2 X 3 X 5 3 X 7 2 X 3 X 3 X 3 3 X 5 X 5

Prime Factorization can be solved with a Factor Tree A factor tree is a model that shows prime factorization.

Example of a factor tree: No matter what factors you use, you will finish with the same answer. Example 1Example X 2 X X 2 X 5

Watch this video Factor Trees

Play These Games y_g_3_t_1.html

Exponents Example: 2 X 2 X 6 X 2 X 6 Combine like terms: 2 X 2 X 2 X 6 X 6 Use exponents: 2³ X 6² 5³ base exponent

How to Write an Exponent Prime factors: 3 x 5 x 5 x 3 x 2 x 5 x 2 Combine like terms: 2 x 2 x 3 x 3 x 5 x 5 x 5 Write down the base numbers: 235 Add exponents (shown in green): However many times you see the base number, that is your exponent. 2²3²5³ Add the multiplication signs: 2² X3² X5³

Play this Game 7 x 7 x 7 8 x 8 7³8²

Do you know your exponents? Take this quiz and record your score in your math journal.

Assessment Click on the following link to complete an assessment on Survey Monkey. _NOT_USE_THIS_LINK_FOR_COLLECTION&sm=Hyhggl7d5 HcJJwK6rcftpN%2b%2fbDp3faTa2fSEgpudJtU%3d We will go over the results in class together.

Definitions Prime number – A number that has only two factors, 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23 Composite number - A number that has more than two factors. Examples: 9 = factors are 1, 3, 9 24 = factors are 1, 2, 3, 4, 6, 8, 12, 24 Exponent – Shows how many times a number, called the base, is used as a factor. (Numbers in green are exponents.) Examples: 3² or 4³ Base – A number used as a factor. (Numbers in red are base numbers.) Examples: 5³ or 6²

GLCE’s N.MR Find the prime factorization of numbers from 2 through 50, express in exponential notation, e.g., 24 = 23 x 31, and understand that every whole number greater than 1 is either prime or can be expressed as a product of primes.*

References Andrews, A.G., Bennett, J. M., Burton, G. M., Johnson, H.C., Luckie, L., Maletsky, E. M., … Schultz, K. A., (2002). Harcourt Math. Orlando: Harcourt School Publishers TION&sm=Hyhggl7d5HcJJwK6rcftpN%2b%2fbDp3faTa2fSEgpudJtU%3d