A number is divisible by eight if it is divisible by two at least three times. To explain this, we can break down the divisibility criteria for eight.
1. Divisible by two: A number is divisible by two if its units digit is even (0, 2, 4, 6, or 8).
2. Divisible by two at least three times: If a number meets the criteria for being divisible by two, then we need to check if it can be divided by two three times. This means that the number must have three factors of 2 in its prime factorization.
For example, let's consider the number 32. The prime factorization of 32 is
, which indeed has three factors of 2. Therefore, 32 is divisible by two at least three times and, consequently, divisible by eight.
Therefore, a number is divisible by eight if it is divisible by two at least three times.