 # Number Theory Divides: b divides a if there is a whole number q such that a = qb. Factor: b will be a factor of a. Divisor: b is also a divisor of a. Multiple:

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Number Theory Divides: b divides a if there is a whole number q such that a = qb. Factor: b will be a factor of a. Divisor: b is also a divisor of a. Multiple: a is a multiple of b.

Multiples Multiples of 2 2x0, 2x1, 2x2, 2x3, 2x4,……… 0, 2, 4, 6, 8,…… Multiples of 3 3x0, 3x1, 3x2, 3x3,….. 0, 3, 6, 9,……..

Divisors or Factors Divisors or Factors of 6: We need to find whole numbers b & q such that 6 = bq Using arrays: 1x 6, 2x3 Rainbow method: 1,2,3,6

Prime & Composite Prime: a natural number that has exactly 2 different factors, namely 1 and itself is prime. Composite: a natural number that has more than 2 different factors is composite. One is called a unit and is neither Prime nor Composite

Primes Sieve of Eratosthenes 2345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626367656667686970 71727374757677787980 81828384858687888990 919293949596979899100

Factor Trees 180 600 675 360

Test for divisibility A number N is divisible by 2 if the last digit is an even digit(0,2,4,6,8). 3 if the sum of the digits is divisible by 3. 5 if the last digit is a 0 or 5. 6 if it is divisible by 2 & 3. 9if the sum of the digits is divisible by 9. 10 if the last digit is 0.

Tell which of the following are divisible by 2,3,5,6,9,or10 43,826 111,111 26,785 5,280

Divisiblity by 11 If the difference between the sums of every other digit is divisible by 11 then the number is divisible by 11. 34,567 343,244 92,252,191,213

Greatest Common Factor (Divisor) The Greatest Common Factor of two numbers m & n will be the number d the divides both m & n at the same time. GCF(m,n) = d GCF(18,45)= ? 18 = {1,2,3,6,9,18} 45 = {1,3,5,9,15,45} F 18  F 45 ={1,3,9} GCF(18,45) = 9

GCF( 24,27) = GCF( 14,27) = GCF(110, 132) =

Using Cuisenaire Rods Pg 265 # 16

Least Common Multiple Least Common Multiple: the smallest common multiple of both m and n is called their Least common Multiple, LCM(m,n) LCM(9,15)= M 9 = {9,18,27,36,45,54,63,72, 81,90,...} M 15 = {15,30,45,60,75,90,105,…} M 9  M 15 = { 45,90,…} LCM(9,15) = 45

Finding GCF & LCM by using Prime Power Representation. Euclidean algorithm.

Homework Pg 241 # 5,6,8a,9 all,11,16,35-39 Pg 253 # 1,5,6,7,8,9,23,24 Pg 265 # 1,2,5,8all,9,17a,31-34

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