Natural Numbers 1 to 32 · Web view... Much Ado About Factors prime factorization of factors factors proper factors composite numbers number sum number sum 175 5 · 5 · 7 1, 5, 7,

Math Backpack document.doc

Natural Numbers 100 to 199 – Tables

Bob & George ● Copyright (c) 2008 by Bob Albrecht ● [email protected]

This reference unit consists of tables of information about the natural numbers 100 to 199.

It is a companion unit to Natural Numbers 100 to 199.

Our number units are posted at www.curriki.org and perhaps elsewhere.

Go to www.curriki.org and search for albrecht number.

If you see a word that you don't know, browse the glossary way down yonder.

Some Special Numbers in the Set of Natural Numbers 100 to 199

Prime numbers: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

Palprimes: 101, 131, 151, 181, 191

Emirps: 107, 113, 149, 157, 167, 179, 199

Peak numbers: 121, 131, 141, 151, 161, 171, 181, 191

Peak primes: 131, 151, 181, 191

Valley prime: 101

Square numbers: 100, 121, 144, 169, 196

Cubic number: 125

Power of 2: 128

Triangular numbers: 105, 120, 136, 153, 171, 190

Factorial number: 120

Fibonacci number: 144

Table 1 (A, B, C, D) is a check list of characteristics of natural numbers 100 to 199: composite, prime, palprime, emirp, deficient, perfect, abundant, square, cubic, power of 2, triangular, factorial, Fibonacci, and atom. The "atom" column lists the atoms that have a number of protons equal to the natural number, from element 100 (fermium, Fm) to element 111 (roentgenium, Rg).

Table 2 (A, B, C, D) lists, for each natural number 100 to 199, the prime factorization of composite numbers, the factors, the number of factors, the sum of the factors, the number of proper factors, and the sum of the proper factors.

Plunge in.

Natural Numbers 100 to 199 – Tables 1 5/6/2023


Table 1A Natural Numbers 100 to 124 Check Listnu

mbe

r

com

posi

te

prim

e

palp

rim

e

emir

p

defic

ient

perf

ect

abun

dant

squa

re

cubi

c

pow

er o

f 2

tria

ngul

ar

fact

oria

l

Fibo

nacc

i

atom

100 x x x Fm

101 x x x Md

102 x x No

103 x x Lr

104 x x Rf

105 x x x Db

106 x x Sg

107 x x x Bh

108 x x Hs

109 x x Mt

110 x x Ds

111 x x Rg

112 x x

113 x x x

114 x x

115 x x

116 x x

117 x x

118 x x

119 x x

120 x x x x

121 x x x

122 x x

123 x x

124 x x



Table 1B Natural Numbers 125 to 149 Check Listnu

mbe

r

com

posi

te

prim

e

palp

rim

e

emir

p

defic

ient

perf

ect

abun

dant

squa

re

cubi

c

pow

er o

f 2

tria

ngul

ar

fact

oria

l

Fibo

nacc

i

atom

125 x x x

126 x x

127 x x

128 x x x

129 x x

130 x x



131 x x x

132 x x

133 x x

134 x x

135 x x

136 x x x

137 x x

138 x x

139 x x

140 x x

141 x x

142 x x

143 x x

144 x x x x

145 x x

146 x x

147 x x

148 x x

149 x x x

Table 1C Natural Numbers 150 to 174 Check List

num

ber

com

posi

te

prim

e

palp

rim

e

emir

p

defic

ient

perf

ect

abun

dant

squa

re

cubi

c

pow

er o

f 2

tria

ngul

ar

fact

oria

l

Fibo

nacc

i

atom

150 x x

151 x x x

152 x x

153 x x x

154 x x

155 x x

156 x x



157 x x x

158 x x

159 x x

160 x x

161 x x

162 x x

163 x x

164 x x

165 x x

166 x x

167 x x x

168 x x

169 x x x

170 x x

171 x x x

172 x x

173 x x

174 x x

Table 1D Natural Numbers 175 to 199 Check List

num

ber

com

posi

te

prim

e

palp

rim

e

emir

p

defic

ient

perf

ect

abun

dant

squa

re

cubi

c

pow

er o

f 2

tria

ngul

ar

fact

oria

l

Fibo

nacc

i

atom

175 x x

176 x x

177 x x

178 x x

179 x x x

180 x x

181 x x x

182 x x



183 x x

184 x x

185 x x

186 x x

187 x x

188 x x

189 x x

190 x x x

191 x x x

192 x x

193 x x

194 x x

195 x x

196 x x x

197 x x

198 x x

199 x x x

Table 2A Natural Numbers 100 to 124 – Much Ado About Factorsprime factorization of factors factors proper factorscomposite numbers number sum number sum

100 2 · 2 · 5 · 5 1, 2, 4, 5, 10, 20, 25, 50, 100 9 217 8 117

101 1, 101 2 102 1 1

102 2 · 3 · 17 1, 2, 3, 6, 17, 34, 51, 102 8 216 7 114

103 1, 103 2 104 1 1

104 2 · 2 · 2 · 13 1, 2, 4, 8, 13, 26, 52, 104 8 210 7 106

105 3 ∙ 5 · 7 1, 3, 5, 7, 15, 21, 35, 105 8 192 7 87

106 2 · 53 1, 2, 53, 106 4 162 3 56

107 1, 107 2 108 1 1

108 2 · 2 · 3 · 3 · 3 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 12 280 11 172



109 1, 109 2 110 1 1

110 2 · 5 · 11 1, 2, 5 10, 11, 22, 55, 110 8 216 7 106

111 3 · 37 1, 3, 37, 111 4 152 3 41

112 2 · 2 · 2 · 2 · 7 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 10 248 9 136

113 1, 113 2 114 1 1

114 2 · 3 · 19 1, 2, 3, 6, 19, 38, 57, 114 8 240 7 126

115 5 · 23 1, 5, 23, 115 4 144 3 29

116 2 · 2 · 29 1, 2, 4, 29, 58, 116 6 210 5 94

117 3 · 3 · 13 1, 3, 9, 13, 39, 117 6 182 5 65

118 2 · 59 1, 2, 59, 118 4 180 3 62

119 7 · 17 1, 7, 17, 119 4 144 3 25

120 2 · 2 · 2 · 3 · 5 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 16 360 15 240

121 11 · 11 1, 11, 121 3 133 2 12

122 2 · 61 1, 2, 61, 122 4 186 3 64

123 3 · 41 1, 3, 41, 123 4 168 3 45

124 2 · 2 · 31 1, 2, 4, 31, 62, 124 6 224 5 100

Table 2B Natural Numbers 125 to 149 – Much Ado About Factorsprime factorization of factors factors proper factorscomposite numbers number sum number sum

125 5 · 5 · 5 1, 5, 25, 125 4 156 3 31

126 2 · 3 · 3 · 7 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 12 312 11 186

127 1, 127 2 128 1 1

128 2 · 2 · 2 · 2 · 2 · 2 · 2 1, 2, 4, 8, 16, 32, 64, 128 8 255 7 127

129 3 · 43 1, 3, 43, 129 4 176 2 47

130 2 · 5 · 13 1, 2, 5, 10, 13, 26, 65, 130 8 252 7 122

131 1, 131 2 132 1 1

132 2 · 2 · 3 · 11 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 12 336 11 204

133 7 · 19 1, 7, 19, 133 4 160 3 27



134 2 · 67 1, 2, 67, 134 4 204 3 70

135 3 · 3 · 3 · 5 1, 3, 5, 9, 15, 27, 45, 135 8 240 7 105

136 2 · 2 · 2 · 17 1, 2, 4, 8, 17, 34, 68, 136 8 270 7 134

137 1, 137 2 138 1 1

138 2 · 3 · 23 1, 2, 3, 6, 23, 46, 69, 138 8 288 7 150

139 1, 139 2 140 1 1

140 2 · 2 · 5 · 7 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140 12 336 11 196

141 3 · 47 1, 3, 47, 141 4 192 3 51

142 2 · 71 1, 2, 71, 142 4 216 3 74

143 11 · 13 1, 11, 13, 143 4 168 3 25

144 2 · 2 · 2 · 2 · 3 · 3 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 15 403 14 259

145 5 · 29 1, 5, 29, 145 4 180 3 35

146 2 · 73 1, 2, 73, 146 4 222 3 76

147 3 · 7 · 7 1, 3, 7, 21, 49, 147 6 228 5 81

148 2 · 2 · 37 1, 2, 4, 37, 74, 148 6 266 5 118

149 1, 149 2 150 1 1

Table 2C Natural Numbers 150 to 174 – Much Ado About Factorsprime factorization of factors factors proper factorscomposite numbers number sum number sum

150 2 · 3 · 5 · 5 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 12 372 11 222

151 1, 151 2 152 1 1

152 2 · 2 · 2 · 19 1, 2, 4, 8, 19, 38, 76, 152 8 300 7 148

153 3 · 3 · 17 1, 3, 9, 17, 51, 153 6 234 5 81

154 2 · 7 · 11 1, 2, 7, 11, 14, 22, 77, 154 8 288 7 134

155 5 · 31 1, 5, 31, 155 4 192 3 37

156 2 · 2 · 3 · 13 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156 12 392 11 236

157 1, 157 2 158 1 1

158 2 · 79 1, 2, 79, 158 4 240 3 82



159 3 · 53 1, 3, 53, 159 4 216 3 57

160 2 · 2 · 2 · 2 · 2 · 5 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160 12 378 11 218

161 7 · 23 1, 7, 23, 161 4 192 3 31

162 2 · 3 · 3 · 3 · 3 1, 2, 3, 6, 9, 18, 27, 54, 81, 162 10 363 9 201

163 1, 163 2 164 1 1

164 2 · 2 · 41 1, 2, 4, 41, 82, 164 6 294 5 130

165 3 · 5 · 11 1, 3, 5, 11, 15, 33, 55, 165 8 288 7 123

166 2 · 83 1, 2, 83, 166 4 252 3 86

167 1, 167 2 168 1 1

168 2 · 2 · 2 · 3 · 7 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 16 480 15 312

169 13 · 13 1, 13, 169 3 183 2 14

170 2 · 5 · 17 1, 2, 5, 10, 17, 34, 85, 170 8 324 7 154

171 3 · 3 · 19 1, 3, 9, 19, 57, 171 6 260 5 89

172 2 · 2 · 43 1, 2, 4, 43, 86, 172 6 308 5 136

173 1, 173 2 174 1 1

174 2 · 3 · 29 1, 2, 3, 6, 29, 58, 87, 174 8 360 7 186

Table 2D Natural Numbers 175 to 199 – Much Ado About Factorsprime factorization of factors factors proper factorscomposite numbers number sum number sum

175 5 · 5 · 7 1, 5, 7, 25, 35, 175 6 248 5 73

176 2 · 2 · 2 · 2 · 11 1, 2, 4, 8, 11, 16, 22, 44, 88, 176 10 372 9 196

177 3 · 59 1, 3, 59, 177 4 240 3 63

178 2 · 89 1, 2, 89, 178 4 270 3 92

179 1, 179 2 180 1 1

180 2 · 2 · 3 · 3 · 5 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 18 546 17 366

181 1, 181 2 182 1 1

182 2 · 7 · 13 1, 2, 7, 13, 14, 26, 91, 182 8 336 7 154



183 3 · 61 1, 3, 61, 183 4 248 3 65

184 2 · 2 · 2 · 23 1, 2, 4, 8, 23, 46, 92, 184 8 360 7 176

185 5 · 37 1, 5, 37, 185 4 228 3 43

186 2 · 3 · 31 1, 2, 3, 6, 31, 62, 93, 186 8 384 7 198

187 11 · 17 1, 11, 17, 187 4 216 3 29

188 2 · 2 · 47 1, 2, 4, 47, 94, 188 6 336 5 148

189 3 · 3 · 3 · 7 1, 3, 7, 9, 21, 27, 63, 189 8 320 7 131

190 2 · 5 · 19 1, 2, 5, 10, 19, 38, 95, 190 8 360 7 170

191 1, 191 2 192 1 1

192 2 · 2 · 2 · 2 · 2 · 2 · 3 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192 14 508 13 316

193 1, 193 2 194 1 1

194 2 · 97 1, 2, 97, 194 4 294 3 100

195 3 · 5 · 13 1, 3, 5, 13, 15, 39, 65, 195 8 336 7 141

196 2 · 2 · 7 · 7 1, 2, 4, 7, 14, 28, 49, 98, 196 9 399 8 203

197 1, 197 2 198 1 1

198 2 · 3 · 3 · 11 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198 12 468 11 270

199 1, 199 2 200 1 1

Glossary

abundant number 1: a natural number n for which the sum of the factors of n is greater than 2n. 2: a natural number n for which the sum of the proper factors of n is greater than n.

composite number 1: a natural number greater than 1 that has factors other than 1 and the number itself. 2: a natural number that has three or more different factors.

cubic number: a number that can be written as the cube of a natural number. Cubic numbers are 1, 8, 27, 64, 125, and so on. [1 = 13, 8 = 23, 27 = 33, 64 = 43, 125 = 53, ....]

deficient number 1: a natural number n for which the sum of the factors of n is less than 2n. 2: a natural number n for which the sum of the proper factors of n is less than n.

emirp 1: a prime number that is the reverse of a different prime number. 2: a prime number obtained by writing the digits of a different prime number in reverse order (right to left instead of left to right). Examples: 37 and 73, 337 and 733, 709 and 907.



factorial number: If n is a natural number, then n factorial, written n!, is the product of the natural numbers from 1 to n. 1! = 1, 2! = 1 ∙ 2 = 2, 3! = 1 ∙ 2 ∙ 3 = 6, 4! = 1 ∙ 2 ∙ 3 ∙ 4 = 24.

factor: If you multiply two natural numbers, the product is a natural number. The numbers you multiplied to obtain the product are factors of the product. If a · b = c, then a and b are factors of c.

Fibonacci number: the numbers 1, 1, 2, 3, 5, 8, 13, and so on. After the second number (1), each number is the sum of the preceding two numbers.

palprime: a prime number that when reversed (read right to left instead of left to right) is the same prime number. Examples: 11, 373, 919.

perfect number 1: a natural number n for which the sum of the factors of n is equal to 2n. 2: a natural number n for which the sum of the proper factors of n is equal to n.

prime number 1: a natural number that has exactly two different factors. 2: a natural number greater than 1 whose only factors are 1 and the number itself.

proper factor: a factor of a natural number other than the number itself. A proper factor of a number is a factor that is less than the number.

natural number: the numbers 1, 2, 3, 4, 5, and so on forever. They keep going and going and going, never ending. Natural numbers are also called counting numbers and positive integers.

square number: a number that can be written as the square of a natural number. Square numbers are 1, 4, 9, 16, 25, and so on. [1 = 12, 4 = 22, 9 = 32, 16 = 42, 25 = 52, .... ]

successor: Every natural number has a successor that is one more than the natural number. If n is a natural number, then its successor is n + 1.

triangular number: the numbers 1, 3, 6, 10, 15, and so on. Triangular numbers greater than 1 can be represented by triangles having 3 dots, 6 dots, 10 dots, 15 dots, and so on.


Documents

Natural Numbers 1 to 32 · Web view... Much Ado About Factors prime factorization of factors factors proper factors composite numbers number sum number sum 175 5 · 5 · 7 1, 5, 7,