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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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prime and composite numbers are all about multiplication
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
Multiplication

factor x factor = product

prime numbers
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 numbers1
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
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 numbers2
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 numbers3
Prime Numbers

A commonmisconception is

that odd numbers

are always prime numbers

but, that’s not true.

prime numbers4
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 numbers5
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 numbers6
Prime Numbers

However, even numbersare never

prime numbers

with one exception—

the number 2.

prime numbers7
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
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 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
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
Only 0 and 1 are neither prime nor composite numbers.

All other whole numbers are either prime or composite numbers.

congratulations
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.