Number Theory Review

x|54363

• x = 3 because the sum of the digits is divisible by 3

• x = 9 because the sum of the digits is divisible by 9

• x = 3 and 9 because the sum of the digits is divisible by 3 and 9

• x is not equal to 3 or 9 because the sum of the digits is not divisible by 3 or 9

x|12456

• x = 2 because its an even number

• x = 4 because the last two digits are divisible by 4

• x = 2 and 4, because its an even number and the last two digits are divisible by 4

• x is not 2 or 4

What is the prime factorization of 540?

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What is the smallest value of n that can be used to make (540)n a perfect square?

What is the smallest value of n that can be used to make (540)n a perfect cube?

When a number is divided by 15, the quotient is 31 and the remainder is 8. What is the number?

• 457

• 263

• 473

• 540

222/d has a quotient of 18 with a remainder of 6, what is the divisor?

When dividing 543 by 11, what is the remainder? Consider using long division.

When dividing 103 by 15, what is the remainder? Consider using the subtraction algorithm.

Let x = An Even Number, what can you tell about 4x + 7?

• It will be Even

• It will be Odd

• You can't tell because you don't know the value of x