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Can you explain why a number that is divisible by 9 is also divisible by 3?
Three is a factor of nine.
A number is divisible by 6 if it is divisible by what numbers?
2 and 3Today, people don't explain why a number has to be divisible by 2 and 3 to be divisible by 6 or how it works.
Explain why the product of any four consecutive integers is divisible by 24?
At least one of the four will be divisible by 4. One other will be divisible by 2 (but not by 4) One other will be divisible by 3. Hence the product will be divisible by 4 x 2 x 3 = 24.
Explain why 21 is not a prime number?
21 has factors other than 1 and itself, so it is not a prime number. For example, it is divisible by 3. (You can check this by adding the digits of the number: 2 + 1 = 3. If the sum of the digits is divisible by 3, the number is also divisible by 3.) Therefore, 21 is a composite number.
If x is an integer divisible by 3 then is x2 divisible by 3?
Yes, if x is an integer divisible by 3, then x^2 is also divisible by 3. This is because for any integer x, x^2 will also be divisible by 3 if x is divisible by 3. This can be proven using the property that the square of any integer divisible by 3 will also be divisible by 3.
