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Factors and Multiples. What are prime numbers?. A prime number is:. If a number has only two different factors, 1 and itself, then the number is said to be prime. For example, 7 = 7 x 1 7 is a prime number since it has only two different factors. Clearly, 2 = 1 x 2 3 = 1 x 3

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Factors and multiples

A prime number is:

If a number has only two different factors, 1 and itself, then the number is said to be prime.


Factors and multiples

For example, 7 = 7 x 1

7 is a prime number since it has only two different factors.

Clearly, 2 = 1 x 2

3 = 1 x 3

5 = 1 x 5

7 = 1 x 7

11 = 1 x 11

Therefore 2, 3, 5, 7, 11… are all prime numbers.



Factors and multiples

A composite number is:

A number that has more than two factors is called a composite number.

For example, 14 = 1 x 14 and 2 x 7

So, 14 is a composite number as it has more than two factors.


Factors and multiples

EXAMPLES

  • State which of the following numbers are prime:

    • 46

    • 19


Factors and multiples

SOLUTION:

  • 46 is not a prime because 46 = 2 x 23.

  • 19 is a prime since it has only two different factors, 1 and 19.


Factors and multiples

FACTORS

‘Factors’ are the numbers you multiply to get another number:

2 x 3 = 6

Factor Factor


Factors and multiples


Factors and multiples


Factors and multiples



Factors and multiples

To test if a number is prime or composite by hand, the easiest thing to do is test if its divisible by prime numbers. If none of them divide it, once the numbers you’re dividing by get bigger than the square root of the number you’re testing, you’re done and know it’s prime.


Factors and multiples

For example, here’s how you would test if 107 is prime: easiest thing to do is test if its divisible by prime numbers. If none of them divide it, once the numbers you’re dividing by get bigger than the square root of the number you’re testing, you’re done and know it’s prime.

  • It’s odd, so it’s not divisible by 2;

  • It’s not divisible by 3 (use the divisibility rule: 1 + 0 + 7 = 8, not 3 or 6 or 9)

  • It’s not divisible by 5 (doesn’t end in 5 or zero)

  • It’s not divisible by 7 (if it were, 107 – 7 = 100 would be divisible by 7, which we know isn’t true)

  • At this point, we know it’s not prime, since we’d need to check 11 next. But 11 x 11 = 121, bigger than 107, so 11 is less than the square root of 107.


Factors and multiples

INTERACTIVE SITE FOR PRIMES AND COMPOSITES easiest thing to do is test if its divisible by prime numbers. If none of them divide it, once the numbers you’re dividing by get bigger than the square root of the number you’re testing, you’re done and know it’s prime.

http://www.321know.com/fra63ax2.htm


Factors and multiples

Sieve of Eratosthenes easiest thing to do is test if its divisible by prime numbers. If none of them divide it, once the numbers you’re dividing by get bigger than the square root of the number you’re testing, you’re done and know it’s prime.

A prime number is a whole number that has exactly two factors, 1 and itself.

We can use the Sieve of Eratosthenes to find out whether a number is prime or composite.

  • The following example illustrates how the Sieve of Eratosthenes, can be used to find all the prime numbers that are less than 100.

  • Step 1: Write the numbers 1 to 100 in ten rows.

  • Step 2: Cross out 1 because 1 is not a prime.

  • Step 3: Circle 2 and cross out all multiples of 2. (2, 4, 6, 8, 10, ...)

  • Step 4: Circle 3 and cross out all multiples of 3. (3, 6, 9, 12, 15, ...)

  • Step 5: Circle 5 and cross out all multiples of 5. (5, 10, 15, 20, ...)

  • Step 6: Circle 7 and cross out all multiples of 7. (7, 14, 21, 28, ...)

  • Circle all the numbers that are not crossed out and they are the prime numbers less than 100.