Divisibility (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

Divisibility: core idea

Basic rules.

Is $483$ divisible by $3$ ? Type $1$ for yes and $0$ for no.

Hint: Apply the relevant digit test or factor condition. Answer: 1.

1. Find the missing digit $x$ so $52x$ is divisible by $9$ .
2. What is the smallest positive multiple of $6$ that is also divisible by $8$ ?
3. How many positive divisors of $24$ are even?
4. Find the remainder when $12345$ is divided by $10$ .
5. Is $731$ divisible by $11$ ? Type $1$ for yes and $0$ for no.
6. What digit makes $4x8$ divisible by $3$ and as small as possible?
7. How many multiples of $7$ are from $1$ through $50$ ?
8. Find the least number to add to $58$ to make a multiple of $5$ .
9. Find the greatest common divisor of $42$ and $56$ .