Prime Factorization

1
Prime Factorization

• 5th Grade Math

2
Prime Factorization Of a Number

• A prime number is a counting number that only has
  two factors, itself and one. Counting numbers
  which have more than two factors (such as six,
  whose factors are 1, 2, 3 and 6), are said to be
  composite numbers. When a composite number is
  written as a product of all of its prime factors,
  we have the prime factorization of the number.
• There are several different methods in which can
  be utilized for the prime factorization of a
  number.

3
Using Division

• Prime factors can be found using division.
• Keep dividing until you have all prime numbers.
  The prime factors of 78 are 2, 3, 13.

4
Remember the Divisibility Rules

• If the last digit is even, the number is
  divisible by 2.
• If the last digit is a 5 or a 0, the number is
  divisible by 5.
• If the number ends in 0, it is divisible by 10.
• If the sum of the digits is divisible by 3, the
  number is also.
• If the last two digits form a number divisible by
  4, the number is also.

5
More divisibility rules

• If the number is divisible by both 3 and 2, it is
  also divisible by 6.
• Take the last digit, double it, and subtract it
  from the rest of the number if the answer is
  divisible by 7 (including 0), then the number is
  also.
• If the last three digits form a number divisible
  by 8, then the whole number is also divisible by
  8.
• If the sum of the digits is divisible by 9, the
  number is also.

6

• Using the Factor Tree
• 78
• / \
• / \
• 2 x 39
• / / \
• / / \
• 2 x 3 x 13

7
Exponents

• 72
• / \
• 8 x 9
• / \ / \
• 2 x 4 x 3 x 3
• / / \ \ \
• 2 x 2 x 2 x 3 x 3

• Another key idea in writing the prime
  factorization of a number is an understanding of
  exponents. An exponent tells how many times the
  base is used as a factor.
• 72 23 x 32

8
Lets Try a Factor Tree!

• 84
• / \
• 2 x 42
• / / \
• 2 x 2 x 21
• / / / \
• 2 x 2 3 x 7
• What is the final factorization?
• 22 x 3 x 7 84

9
Factor Trees do not look the same for the same
number, but the final answer is the same.

• 72
• / \
• 8 x 9
• / \ / \
• 2 x 4 x 3 x 3
• / \
• 2 x 2 x 2 x 3 x 3

• 72
• / \
• 2 x 36
• / / \
• 2 x 2 x 18
• / / / \
• 2 x 2 x 2 x 9
• / / / / \
• 2 x 2 x 2 x 3 x 3

10
Greatest Common Factors

• One method to find greatest common factors is to
  list the factors of each number. The largest
  number is the greatest common factor.
• Lets find the factors of 72 and 84.
• 72
• 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
• 84
• 1, 2, 3, 4, 6, 12, 14, 21, 28, 42, 84

11
Prime Factorization is helpful for finding
greatest common factors.

• 72
• / \
• 8 x 9
• / \ / \
• 2 x 4 x 3 x 3
• / \
• 2 x 2 x 2 x 3 x 3
• Take the common prime factors of each number and
  multiply to find the greatest common factor.

• 84
• / \
• 2 x 42
• / / \
• 2 x 2 x 21
• / / / \
• 2 x 2 3 x 7
• 2 x 2 x 3 12

12
Resources

• Brain Pop Prime Factors
• Brain Pop - Prime Numbers
• Brain Pop - Exponents

13
Standards

• Checks for Understanding
• 0506.2.2    Use the prime factorization of two
  whole numbers to determine the greatest common
  factor and the least common multiple.
• 0506.2.2    Use the prime factorization of two
  whole numbers to determine the greatest common
  factor and the least common multiple.
• 0506.2.4    Use divisibility rules to factor
  numbers.
• 0506.2.10  Use exponential notation to represent
  repeated multiplication of whole numbers.
• Grade Level Expectations
• GLE 0506.2.2    Write natural numbers (to 50) as
  a product of prime factors and understand that
  this is unique (apart from order).