Select the correct answerWhat is the highest power of 12 that divides 54!?radio_button_unchecked50radio_button_unchecked25radio_button_unchecked26radio_button_unchecked51

The highest power of 12 that divides 54! is 26.

Here's how you can find it:

First, we need to find the highest power of 2 and 3 (since 12 = 223) that divides 54!.

For 2: 54/2 = 27 54/4 = 13.5 (we only consider the integer part, so 13) 54/8 = 6.75 (we only consider the integer part, so 6) 54/16 = 3.375 (we only consider the integer part, so 3) 54/32 = 1.6875 (we only consider the integer part, so 1) 54/64 = 0.84375 (we only consider the integer part, so 0) Adding these up, we get 27+13+6+3+1 = 50. So, the highest power of 2 that divides 54! is 50.

For 3: 54/3 = 18 54/9 = 6 54/27 = 2 Adding these up, we get 18+6+2 = 26. So, the highest power of 3 that divides 54! is 26.

Since 12 = 223, we need to find the minimum of the highest power of 2 and 3 that divides 54!. The minimum of 50 and 26 is 26. So, the highest power of 12 that divides 54! is 26. Therefore, the correct answer is 26.