Number Properties

Question 1

An integer is divisible by 2 if…

Answer 1

The integer is even

OR

The integer ends in 0, 2, 4, 6, 8

Question 2

An integer is divisible by 3 if…

Answer 2

The SUM of the integer’s DIGITS is divisible by 3.

Question 3

An integer is divisible by 4 if…

Answer 3

The integer is divisible by 2 TWICE

OR

If the LAST TWO DIGITS of the integer are divisible by 4.

Question 4

An integer is divisible by 5 if…

Answer 4

The integer ends in 0 or 5.

Question 5

An integer is divisible by 6 if…

Answer 5

The integer is divisible by BOTH 2 and 3.

Question 6

An integer is divisible by 8 if…

Answer 6

The integer is divisible by 3 THREE TIMES

OR

If the LAST THREE DIGITS of the integer are divisible by 8.

Question 7

An integer is divisible by 9 if…

Answer 7

The SUM of the integer’s DIGITS is divisible by 9.

Question 8

An integer is divisible by 10 if…

Answer 8

The integer ends in 0.

Question 9

What is special about adding/subtracting together two numbers with the same multiple?

Answer 9

If you add or subtract multiples of N, the result (sum or difference) is a multiple of N.

Question 10

What is the only even prime number?

Answer 10

2

Question 11

What is the Factor Foundation Rule?

Answer 11

This rule states that if A is a factor f B, and B is a factor of C, then A is a factor of C.

In other words, an integer is divisible by all of its factors, and it is also divisible by all the factors of its factors.
–> Ex: 72 is divisible by 12, therefore it is divisible by all the factors of 12 (1, 2, 3, 4, 6, 12)

Question 12

How can you determine if a the sum or difference of two numbers will be odd or even?

Answer 12

Add or subtract 2 ODDS or 2 EVENS, the result is EVEN.

Add or subtract an even with an odd, the result is ODD.

Question 13

How can you determine if the product of multiple integers is odd or even?

Answer 13

When multiplying integers, if ANY of the integers are EVEN then the result is EVEN.

Likewise, if NONE of the integers are even then the result is ODD

**NOTE if there are TWO even integers in a set of integers, the result will be divisible by 4. If there are THREE even integers in a set of integers, the result will be divisible by 8.

Question 14

Is the sum of any two Prime numbers (excluding 2) an even or odd number?

Answer 14

Since all Prime numbers are ODD (except 2), then the sum will be even since ODD + ODD = EVEN.

Question 15

How do you represent odd and even numbers Algebraically?

Answer 15

Even numbers are multiples of 2, so an even number can be written as 2n

Odd numbers are one more or less than multiples of 2, so an odd number can be written as (2n + 1) or (2n - 1)

Question 16

In Combinatorics and Probability, what do the words “OR” and “AND” represent?

Answer 16

OR = add

AND = multiply