Track / Stage 4 / 322 of 340 #582 of 1964

Problem 582

AMC 12 late, AIME early

Number theory Difficulty 5.0 Find the answer

8. Among the following four numbers $1307674368000$ , $1307674368500$ , $1307674368200$ , $1307674368010$ , only one is the product of the integers from 1 to 15. This number is ( ). Note: Comprehensive application of divisibility

Your answer

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

【Analysis】Observation shows that among the four numbers above, only the last three digits are different.
In 15! : the number of 2s is 11; the number of 5s is 3, so there must be 3 zeros at the end, making this number 1307674368000

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.