Is 140 x 141 x 142 x 143 x 144 x 145 x 146 x 147 x 148 x 149 x 150 x 151 x 152 x 153 x 154 x 155 x 156 x 157 x 158 x 159 x 160 divisible by 4321?

Answer 1

Yes

(145 x 149) is a factor of 140 x 141 x ... x 145 x ... x 149 x ... x 160

145 = 5 x 29

⇒ 145 x 149 = 5 x 29 x 149

= 5 x 4321

so 4321 is a factor of 145 x 149, thus is also a factor of 140 x 141 x ... x 160 and so 4321 divides 140 x 141 x ... x 160