4-26th grade math

Prime Factorization

Objective

• To use divisibility rules to check for divisibility and write the prime factorization of numbers in exponential form.

• Why? To help you with prime factoring, simplifying fractions, division.

California State Standards NS 1.4 (Gr. 5): Determine the prime factors of

all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show the multiples (e.g., 24 = 2 x 2 x 2 x 3 = 2³ x 3)

MR 3.3: Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.

Vocabulary• Divisible – A number is divisible by another number if the remainder is

zero after dividing.• 36 ÷ 6 = 6

• Prime Number– A whole number greater than one with only two factors-

itself and one.• 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 57, 59, …

• Composite Number– A whole number greater than one that has more than two

factors• 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, …

• Prime Factorization– Writing a number as the product of its prime factors

• 24 = 2 x 2 x 2 x 3

Divisibility Rules! Divisibility Rules

A number is divisible by:

2 If the last digit ends in 0, 2, 4, 6, 8 (any even number)

3 If the sums of the digits is divisible by 3 (may be even or odd)

4 If the last two digits are divisible by 4 (only an even number)

5 If the last digit ends in 0 or 5 (any number ending in 5 or 0)

6 If the number is divisible by 2 and 3 (only an even number)

9 If the sum of the digits is divisible by 9 (may be even or odd)

10 If the last digit ends with a 0 (only ends in 0)

How To Prime Factor - #1• Make a ‘Factor Tree’ 40 2 x 20 5 x 4

2 x 2 = 2³ x 5Factor out each number until you get only primesCircle the prime numbers to be organizedPut final answer in exponential form

How to Prime Factor- #2Make a ‘Factor Ladder’

Put the number at the top of a ‘ladder’= box

If it is even, begin ÷ 2 If not, try greater primes like 3,

5, 7, 9Only move on when the current

number you are using doesn’t work anymore

Use the divisibility rules to helpThe numbers on the side of the

ladder are the numbers used for prime factorization.

prime factor 40

= 2³ x 5

40

2 20

2 10

2 5

Try It!Tell if each number is divisible by:

2, 3, 4, 5, 6, 9,or 10

1) 3,742

2) 5,310

3) 47,388

4) 9,999

5) 41, 112

1) 2

2) 2, 3, 5, 6, 9, 10

3) 2, 3, 4, 6

4) 3, 9

5) 2, 3, 4, 6, 9

Try Some More!

Use exponents to write the prime factorization of each number.

1) 64

2) 48

3) 76

1)

64 = 2⁶2)

48 = 2⁴ x 3

64

2 32

2 16

2 8

2 4

2 2

48

2 24

2 12

2 6

2 3

3)

76 = 2² x 19

76

2 38

2 19

More to TryPrime factor using exponents.

9) 81

10) 90

9)

81 = 3⁴

10)

90 = 2 x 3² x 5

81

9 9

3x3 3x3

90

9 10

3 x 3 5 x 2

Objective Review

• To use divisibility rules to check for divisibility and write the prime factorization of numbers in exponential form.

• Why? You can now prime factor efficiently, simplify fractions, and divide better

Independent Practice

• Complete problems 12-23

• Copy original problem first.

• Show all work!

• If time, complete Mixed Review: 24-29

• If still more time, work on Accelerated Math.