Prime numbers Composite numbers Neither prime nor composite How to know?

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# Prime numbers Composite numbers Neither prime nor composite How to know? - PowerPoint PPT Presentation

Prime numbers Composite numbers Neither prime nor composite How to know?. Prime and composite numbers are all about multiplication. Multiplication math vocabulary: The two numbers being multiplied together are each called factors .

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Presentation Transcript
Prime and composite numbers are all about multiplication

Multiplication math vocabulary:

The two numbers being multiplied together are each called factors.

The answer in a multiplication problem is called the product.

Multiplication

factor x factor = product

Prime Numbers

To determine

if a number is a prime number,

place it in the product position.

=

X

Factor

Factor

Product

Is this number a prime number?

Prime Numbers
• Must have ONLY two possible, unique factors. (Both factors cannot be the same.)
• One factor must be 1.
• One factor must be a whole number, but not 0 or 1.

Factor

same number as the product,

but not 0 or 1.

X

Factor

1

=

Product

same number as one of the factors,

but not 0 and not 1

Whole numbers

In case you forgot:

Whole numbers are the

the number0, and the natural numbers which start at positive one— {0, 1, 2, 3...}

Prime Numbers

3

same number as the product,

but not 0 or 1.

X

1

=

3

same number as one of the factors,

but not 0 and not 1

3 is a prime number.

• There are ONLY two possible, unique factors.

(No other two numbers multiplied together have a product of 3 and both factors are different numbers.)

2. One factor is 1.

3. One factor is a whole number, but not 0 or 1.

Prime Numbers

A commonmisconception is

that odd numbers

are always prime numbers

but, that’s not true.

Prime Numbers

Some odd numbers,

like 9 have more than

two factors.

9 x 1 = 9,

but so does3 x 3.

Consequently,9 is not a prime number.

Prime Numbers

51 is tricky!

It is an odd number.

It looks like only 51 x 1 = 51, but

17 x 3 = 51 too.

51is not a prime number.

HINT:Divisibility rules and multiplication tables can help you discover that a number that seems like a prime number really isn’t.

Prime Numbers

However, even numbersare never

prime numbers

with one exception—

the number 2.

Prime Numbers

2is aprime number,

because the only two factors

of 2

are 2 x 1 = 2.

Every other even number has 2 as a factor too (that’s why no other even number is a prime number).

Composite Numbers

Numbers

with more than two factors are called composite numbers.Numbers that aren’t prime numbers are composite numbers.

The special case of the number 1

The number 1 is

nota prime number and,

it isnota composite number.

Why? because, the number 1only has one factor, nottwo different factors.

1 x 1 = 1

The special case of the number 0.

Zero is another special number.

Zero can not be a prime number because,

every number is a factor of 0.

0 x 1 does equal 0, but

0 x anything at all = 0

Zero is not a composite number either.

Only 0 and 1 are neither prime nor composite numbers.

All other whole numbers are either prime or composite numbers.

Congratulations!

That’s how to tell a prime number from a composite number.

Remember, if in doubt; with big numbers, use divisibility rules.

With smaller products, use multiplication tables.

And all even numbers, except 2, are always composite.