LET Reviewer: Mathematics - MULTIPLES

The MULTIPLES of a number are those numbers that are divisible by the given number.
Characteristics: 

1. A number has an infinite number of multiples. 

2. A number is always a multiple of itself.

Example: The multiples of 3 are 3, 6, 9, 12, 15...

DIVISIBILITY are ways of quickly determining factors without having to perform a complete division.

Divisibility Test for 2
A number divisible by 2 is an even number. Example: 300, 12, 254, 1008

Divisibility Test for 3
A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
Example: 186585 is divisible by 3 because 1+8+6+5+8+5 = 33, and 33 is divisible by 3.

Divisibilty Test for 4
If the number formed by its last 2 digits is divisible by 4.
Example: 128 & 524 are divisible by 4, since 28 and 24 are divisible by 4.

Divisibility Test for 5
If the ones digit is 0 or 5, then the number is divisible by 5.
Example: 300, 505, 2090

Divisibility Test for 6
If it is an even number and divisible by 3.
Example: 634128 is an even number. 6+3+4+1+2+8 = 24, and 24 is divisible by 3.

Divisibility Test for 7
Steps:
1. Double the last digit.
2. Subtract the product in step 1 from the number without the last digit.
3. If the difference is a multiple of 7, then the number is divisible by 7.
Note: if the difference is big, repeat steps 1 to 3.
Example: Is 6853 divisible by 7?
Solution: 1. 3(2) = 6 2. 685-6 = 679
3. (Repeat 1&2) 9(2) = 18
4. 67 - 18 =49 is divisible by 7.

Divisibility Test for 8
If the last digit of a number is divisible by 8.
Example: 4912, the last 3 digits are 912 & 912 = (114)(8)

Divisibility Test for 9
If the sum of its digits is a multiple of 9.
Example: 845721, 8+4+5+7+2+1 = 27

Divisibility Test for 10
If any number except 0 ends in 0.
Example: 3,000; 10,000; 200

Divisibility Test for 11
If after subtracting and adding the digits successively.
Example: 4972, 4-9+7-2 = 0, 0 is divisible by 11.