MATH Test 3

1. 4 prime factors 2. 2 x 5 x 3 x 2 = 60 TOTAL

1. How many PRIME factors in 3 x 5^4 x 11^2 x 13? 2. How many factors in 3 x 5^4 x 11^2 x 13?

12: 2 factors 48: 2 factors

How many PRIME factors in 12 and 48?

smallest positive common multiple of A and B

LCM

every composite number has a prime factorization; n = P1 ^ N1 x P2 ^ N2 x P3 ^ N3.... P = prime numbers N = composite numbers

THEOREM

n = counting number; F = largest whole number such that F^2 < n if a prime number is LESS THAN or equal to F divides N, then N is COMPOSITE if no prime numbers less than or equal to F divides N, then N is a PRIME

Theorem 14 ( Square Root Test )

1. prime 2. neither 3. composite 4. neither 5. prime

PRIME / COMPOSITE / NEITHER 1. 11 2. 1 3. 24 4. 0 5. 103

1: a number that ONLY HAS 2 FACTORS (1 and itself) 2: it's ONLY divisors are 1 and itself 3: 1 IS NOT PRIME; 2 is the smallest prime # 4: must be "counting number", no negatives

Prime Numbers DEFINITION

12< 3, 4 < 3 / 2, 2 facotrs= 2^3 x 3 48< 8, 6 < 4, 2 / 3, 2 < 2, 2, 2 / 3, 2 factors = 2^4 x 3

TREE FACTORIZATION 1. 12 2. 48

numbers that can be multiplied by more than 1 and itself ex: 4 because 2 x 2 = 4

Composite Numbers DEFINITION

12: 1, 2, 3, 4, 6, 12 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

How many factors in 12 and 48?

2 x (3^2 x 3^2) x 5^2 x 11 (broke up 3^4 into 3^2) [2 x 3^2] x 3^2 x 5^2 x 11 [2 x 9] 18 YES ITS A FACOTOR

Is 18 a factor of 2 x 3^4 x 5^2 x 11 ?

120: 2^3 x 3 x 5 36: 2^2

LCM (120, 36) prime factorization

3: 3, 6, 9, 12, 15**, 18 5: 5, 10, 15**, 20 LCM=15

LCM (3, 5) list method

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37...

List some prime numbers....