Final answer:
The largest number that goes into 81 and 48 is 3.
Step-by-step explanation:
To find the largest number that goes into 81 and 48, we need to find the greatest common divisor (GCD) of these two numbers. One way to find the GCD is to factorize both numbers and then find the highest power of any common prime factor.
81 can be factored into 3 * 3 * 3 = 3^4
48 can be factored into 2 * 2 * 2 * 2 * 3 = 2^4 * 3
The highest power of 3 that is a common factor is 3^1. Therefore, the largest number that goes into 81 and 48 is 3.