Divisibility Rules
A number is divisible by
2
3
4
5
6
10
if
the number is even (ends in 2, 4, 6, 8, 0)
the sum of the digits is divisible by 3
the last two digits are divisible by 4
the number ends in a 5 or 0
the number is divisible by 2 and 3
the number ends with a 0
Multiples
Multiples are the product of a counting number and another number.
The multiples of 2 include 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26…
The multiples of 3 include 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36…
The multiples of 4 include 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52…
The multiples of 5 include 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65…
The multiples of 6 include 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78…
The multiples of 7 include 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91…
The multiples of 8 include 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104…
The multiples of 9 include 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117…
The multiples of 10 include 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130…
The multiples of 11 include 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143…
The multiples of 12 include 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156…
The multiples of 13 include 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169…
Factors
Factors are the numbers multiplied together to get a product.
The factors of a particular number are numbers multiplied together to get that particular number.
The factors of 2 are 1, 2.
The factors of 3 are 1, 3.
The factors of 4 are 1, 2, 4, because 1x4 and 2x2 equal 4.
The factors of 5 are 1, 5.
The factors of 6 are 1, 2, 3, 6, because 1x6 and 2x3 equal 6.
The factors of 7 are 1, 7.
The factors of 8 are 1, 2, 4, 8, because 1x8 and 2x4 equal 8.
The factors of 9 are 1, 3, 9, because 1x9 and 3x3 equal 9.
The factors of 10 are 1, 2, 5, 10, because 1x10 and 2x5 equal 10.
The factors of 11 are 1, 11.
The factors of 12 are 1, 2, 3, 4, 6, 12, because 1x12, 2x6, and 3x4 equal 12.
The factors of 13 are 1, 13.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, because 1x24, 2x12, 3x8, and 4x6 equal 24.
The factors of 50 are 1, 2, 5, 10, 25, 50, because 1x50, 2x25, and 5x10 equal 50.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64, because 1x64, 2x32, 4x16, and 8x8 equal 64.
Prime and Composite Numbers
Prime Numbers are counting numbers greater than 1 whose only two factors are 1 and itself.
2 is a prime number, because its only factors are 1 and 2.
3 is a prime number, because its only factors are 1 and 3.
5 is a prime number, because its only factors are 1 and 5.
7 is a prime number, because its only factors are 1 and 7.
11 is a prime number, because its only factors are 1 and 11.
13 is a prime number, because its only factors are 1 and 13.
Composite numbers are counting numbers greater than 1 that are divisible by a number other
than itself and one. Every composite number has three or more factors.
4 is a composite number, because it has three or more factors (1, 2, 4).
6 is a composite number, because it has three or more factors (1, 2, 3, 6).
8 is a composite number, because it has three or more factors (1, 2, 4, 8).
Suggestions for Practice with Parents
Practice does not only have to occur during homework time. It can happen during down time,
like when you and your scholar are riding in the car or when your scholar is washing dishes.
Divisibility Rules: State a number and ask if it is divisible by 2, 3, 4, 5, 6, or 10.
Example: Is 315 divisible by 3? How do you know? Is 315 divisible by 5?
Multiples: Ask them to list the multiples of a certain number.
Example: List the multiples of 7 until I stop you.
Encourage higher numbers than their times tables, especially if they are useful in everyday ways.
Example: What are the multiples of 25 (counting quarters)? What are the multiples of 15
(quarters of an hour)? What are the multiples of 20 (counting $20 bills)?
Follow up a simple number with that same number multiplied by ten or one hundred.
Example: What are the multiples of 8? What are the multiples of 80? What are the multiples of
800? What are the multiples of 8000?
Use numbers that will help the scholar track both the hundreds place and the tens or ones place.
Example: What are the multiples of 103?
You can also use fractions or decimals.
Example: Count by fourths. One-fourth, two-fourths, three-fourths, one, one and one-fourth…
Factors and Prime/Composite Numbers
Ask your scholar to name the factors for a certain number. Ask them how many factors that
number had. Then ask if the number is prime or composite.
Example: What are the factors of 9? (1, 3, 9) How many factors does 9 have? (3) Is 9 a prime
or composite number? (composite)