一道5年级数学题, 提问

数学老师发EMAIL给我, 儿子作业时间太少, 要我监督, 检查.

今早餐前, 打开作业, 就查了一道题, 是他的书上的练习题目,我也有点蒙了. The problem likes this (in my words),

One kid found a way to calculate the number of factors of a number from find out exponents of prime factors. eg:

40=( 2^3) * (5 ^1 ),  exponent of prime number 2 is 3, exponent of 5 is 1, so the number of factors=(3+1)*(1+1)=8,

so 40 total has 8 factors.

Is it correct? Can you find a counter example?

我儿子找了个反例, ---15,  但我说儿子错了. 可是我却找不到反例也不确定这方法的正确性, 儿子就上学去了.
我验算了下面 :
 900=2^2 * 3^2 *5 ^2
from the formula, get the total number of factors,
 (2+1)*(2+1)*(2+1)=27,
there's 27 factors.  I find factors:
1, 2, 3, 4, 5, 6, 9, 10, 12, 15,
18, 20, 25, 30, 36, 45, 50, 60,75, 90,
100, 150, 180, 225, 300, 450, 900. 

27个, 也是对的呀.  那位大拿 帮帮忙, 上面方法及公式对吗?