Review Basic Math Divisibility tests Prime and Composite Numbers

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Review Basic Math Divisibility tests Prime and Composite Numbers Prime Factorization

Multiplication is repeated addition with a different notation. 4 + 4 + 4 + 4 + 4 = 5 x 4 = 20 5 fours factor product

Helpful Hint Remember a factor is any number that divides a number evenly (with a remainder of 0). Give all factors of 32:

Divisibility Tests A whole number is divisible by 2, if its last digit is 0, 2, 4, 6, or 8. 3, if the sum of its digits is divisible by 3. 196 is divisible by 2 117 is divisible by 3 (1+1+7=9!)

Divisibility Tests . . . A whole number is divisible by 5, if the last digit is 0 or 5. 10, if its last digit is 0. 2,345 is divisible by 5. 8,470 is divisible by 10.

Divisibility Tests . . . A whole number is divisible by 4, if the number represented by the last two digits of a whole number is divisible by 4 6, if it is divisible by 2 and 3 2,344 is divisible by 4 (44 is divisible by 4) 8,460 is divisible by 6 (check both tests)

Divisibility Tests . . . A whole number is divisible by 8, if the number represented by the last three digits of a whole number is divisible by 8 9, if sum of its digits is divisible by 9 2,064 is divisible by 8 (064 is divisible by 8) 8,460 is divisible by 9 (8+4+6+0= 18)

Prime and Composite Numbers A prime number is a natural number greater than 1 whose only factors are 1 and itself. The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ... A composite number is a natural number greater than 1 that is not prime. Examples: 4, 12, 9,…

The natural number 1 is neither prime nor composite. Helpful Hint What kind of number is 1? (Prime, composite or neither?) The natural number 1 is neither prime nor composite.

Prime Factorization A prime factorization of a number expresses the number as a product of its factors and the factors must be prime numbers.

Helpful Hint Remember a factor is any number that divides a number evenly (with a remainder of 0).

Every whole number greater than 1 has exactly one prime factorization. Unique Prime Factorization Theorem Every whole number greater than 1 has exactly one prime factorization. 12 = (4)(3) = 2 • 2 • 3 12 = (6)(2) = 3 • 2 • 2 2 and 3 are prime factors of 12 because they are prime numbers and they divide evenly into 12