Prime Factorization

Factors Factors: numbers that multiply together to make another number ex: 1, 2, 3, 6 are factors of the number 6, because they all can multiply to make 6 ex: 1, 2, 3, 4, 12 are factors of the number 12, because they all can multiply to make 12 Factor Pairs: two numbers that multiply to a particular number ex: 1,8 ; 2,4; are factor pairs of the number 8, with these pairs the product is 8 ex: 1•24 ; 2•12 ; 3•8; 4•6 are factor pairs of the number 24

Prime vs Composite vs Neither Prime Number: divisible by 1 and itself, therefore has exactly two factors. ex: 2, 3, 5, 7, 11, 13, 17, 19 Composite Number: has more than two factors. ex: 4, 6, 8, 9, 10, 12, 14, 15, 16 Neither: not prime, not composite. 0 and 1 are the only neithers

Divisibility Rules Rules to help us determine if numbers are prime or composite. If a number can be divided by numbers other than 1 and itself, then it is a COMPOSITE number If a number cannot be divided by other numbers (except 1 and itself) then it is PRIME

Divisibility Rules 2 – last digit of the number must be even (0,2,4,6,8) ex: 20, 34, 52, 68, 96 ex: 312 3+1+2 = 6 can we divide 6 by 3 evenly? Yes, so, 312 is divisible by 3. 3 – add the digits, if the sum is divisible by 3 ex: 624 last 2 digits makes 24, 24 is divisible by 4, so 624 is too 4 – if the last 2 digits as a number can be divided by 4 5 – if the last digit is a 0 or a 5 ex: 25, 30, 35, 40 6 – if the rules for 2 and 3 work, then it’s divisible by 6 ex: 12, its even and divisible by 3 ex: 882 8+8+2 = 18 can we divide 18 by 9 evenly? Yes, so, 882 is divisible by 9. 9 – add the digits, if the sum is divisible by 9 10 – last digit ends in 0 ex: 10, 20, 1000

Factor Tree 30 30 10 3 15 2 5 2 3 5 3 2 Or 5 2 3 (works either way) A factor tree is a math drawing that breaks down a number into its prime factors 30 30 Or (works either way) 10 3 • 15 2 • 5 2 3 • • 5 3 2 • • Prime Factorization of 30 = 5 • 2 • 3 *Prime Factorization results in only prime numbers. *1 is a “neither” number, therefore cannot be on a factor tree or in a prime factorization.