Question

Agent Sanchez must enter a code on a keypad to unlock the door to her office. If the fourth digit of the code in September is 2 more than the fourth digit of the code number based on the prime factors of 225, then the prime factors of which number were used for the code?

a) 27
b) 64
c) 225
d) 512

Answer 1

To unlock the door, Agent Sanchez used the prime factors 3^2 * 5^2, which is equivalent to 225.

Step-by-step explanation:

The student asked about the prime factors of a certain number and how they relate to a code Agent Sanchez uses. To determine the prime factors of 225, we decompose 225 into prime numbers. The fourth digit of the code in September is 2 more than the fourth digit of the code number based on the prime factors of 225. To find the prime factors of 225, we can perform prime factorization. The prime factorization of 225 is 3^2 * 5^2.

Now, let's find the fourth digit of the code number based on the prime factors: 2 + 2 = 4.

Therefore, the prime factors of the code used for the keypad are 3^2 * 5^2, which is equivalent to 225.