Divisibility Rules, Factors and Prime Factors

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Divisibility Rules, Factors and Prime Factors
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What is the object below called?
How do you find the area of this rectangle?
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The area of a rectangle is found by multiplying
the length of the rectangle by the width of the
rectangle.
2
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The area is 12.
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Multiplying any two numbers is the same as
finding the area of a rectangle that has those
same dimensions.
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Can you find the dimensions of every rectangle
that has an area of 36?
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(No Transcript)
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The pairs of numbers that make-up the dimensions
of each rectangle are called the factors of 36.
The factors of 36 are
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A seamstress has 30 square pieces of material to
sew together in a rectangular design. What are
her options?
These numbers are the factors of 30.
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What are the factors of 24?
What are the factors of 48?
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How do you know if a number has a factor of 2?
of 3?
of 4?
of 7?
of 5?
of 8?
of 6?
of 9?
of 10?
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There is a set of rules that helps
mathematicians to to find some of the
smallest factors.
These rules are called
the Divisibility Rules.
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The Divisibility Rules

• Numbers that are evenly divisible by 2 always end
  in 0, 2, 4, 6, or 8.

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The Divisibility Rules

• Numbers that are evenly divisible by 3 can be
  found by adding the digits of the number to see
  if it is a multiple of 3.

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The Divisibility Rules

• Numbers that are evenly divisible by 5 end in 5
  or 0.

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The Divisibility Rules

• Numbers that are evenly divisible by 6 exist only
  if 2 and 3 are divisible evenly.

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The Divisibility Rules

• Numbers that are evenly divisible by 9 can be
  found by adding the digits of the number to see
  if it is a multiple of 9.

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The Divisibility Rules

• 10 Numbers that are evenly divisible by 10 end in
  0.

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The Divisibility Rules

• Numbers that are evenly divisible by 2 always end
  in 0, 2, 4, 6, or 8.
• Numbers that are evenly divisible by 3 can be
  found by adding the digits of the number to see
  if it is a multiple of 3.
• Numbers that are evenly divisible by 5 end in 5
  or 0.
• Numbers that are evenly divisible by 6 exist only
  if 2 and 3 are divisible evenly.
• Numbers that are evenly divisible by 9 can be
  found by adding the digits of the number to see
  if it is a multiple of 9.
• 10 Numbers that are evenly divisible by 10 end in
  0.

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Is 72 divisible by . . .
yes
2?
yes
3?
no
5?
yes
6?
yes
9?
no
10?
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The divisibility rules helped to find the
factors of 2,3,6 and 9. How do we find the rest
of the factors?
Long division.
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Divisibility rules do not cover all numbers.
Always test 4 and 7 through long division.
The factors of 72 are . . .
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Prime Factors
A number is prime if it only has two factors, 1
and itself. A number that is not prime is called
composite.
Examples of prime numbers are . . .
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Prime Factorization
The prime factorization of a number is to rewrite
the number as a product of only prime factors.
Click here.
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Once a number has been completely factorized, the
prime factors should be written as a product.
The prime factorization of 24 is . . .