2. Use the ladder method to find the prime These numbers. \( \begin{array}{ll}\text { a) } 120 & \text { b) } 78 \\ \text { c) } 154 & \text { d) } 200 \\ \text { e) } 186 & \text { f) } 99\end{array} \)

To find the prime factors using the ladder method, start with the number at the top left of the ladder. For 120, you can divide by 2 to get 60, then again by 2 to get 30, and again by 2 to get 15. After that, switch to 3 to get 5. This gives you the prime factors: \( 2^3 \times 3 \times 5 \). For 78, the ladder method can start with dividing by 2 to get 39, and then switch to 3 to get 13, resulting in \( 2 \times 3 \times 13 \). For the others: 154 can be divided by 2 and then 7 to yield \( 2 \times 7 \times 11\), while 200 gives \( 2^3 \times 5^2 \). The ladder for 186 starts with 2 to yield 93, then 3 to 31, so you get \( 2 \times 3 \times 31 \). Lastly, for 99, you first divide by 3 to get 33, then by 3 again for 11, giving \( 3^2 \times 11 \). Happy factoring!