What is the remainder when 1271 * 1275 * 1279 *1285 is divided by 12? Choose the most appropriate option: A) 0 B) 1 C) 11 D) 3 E) 7
1271*1275*1277*1285 = (1272 - 1)(1272 + 3)(1284 - 5)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)   Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-1)(3)(-5)(1) = 15. Thus the question becomes: what is the remainder upon division of 15 by 12? The answer to this question is 3   Answer: 3.
<result>D</result>
What is the remainder when 1271 * 1275 * 1279 *1285 is divided by 12?