Graduate Management Admission Test (GMAT) Practice Test

Any number that is divisible by 8 is also divisible by which of the following?

1. 6 and 3

2. 4 and 2

3. 5

4. Only 2

The correct answer is: 4 and 2

A number is considered divisible by another number if dividing it by that number results in an integer with no remainder. When a number is divisible by 8, it means it can be expressed as 8 multiplied by some integer. The key is to examine the factors of 8 to determine what other numbers it is divisible by. The number 8 can be factored into primes as \(2^3\). This indicates that 8 contains three factors of 2. Consequently, any multiple of 8 will also have at least two factors of 2, which means it is also divisible by 4 (since \(4 = 2^2\)) and by 2. To see this more clearly, consider that: - If a number \(n\) is divisible by 8, then \(n = 8k\) for some integer \(k\). - Since \(8 = 4 \times 2\), it follows that \(n\) can be expressed as \(n = 4 \times (2k)\), indicating that \(n\) is divisible by 4. - Additionally, since \(n\) also has at least one factor of 2, it is certainly divisible by 2