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Alfredo Perez
Resident Mathematician
Texas A&M University
GK-12 Program
• Factorization is a very important concept
in mathematics
• Before learning factorization, you must
become familiar with the rules of divisibility
• By knowing divisibility rules, you can find
the factors of any number very easily!
The most important to know…
A NUMBER IS DIVISIBLE BY
2
3
IF the last digit is even (0,2,4,6, or 8)
4
5
6
8
IF the last two digits together can be divided by 4
9
IF the sum of all the digits gives a number that can be
divided by 9
10
IF the sum of all the digits gives a number that can be
divided by 3
IF the last digit is a 5 or a 0
IF the number is divisible by both 2 and 3
IF the last three digits together can be divided by 8
IF the last digit is a 0
RECALL: All numbers are divisible by 1
12,632
Divisible by 2 because the number is even
14,361
Divisible by 3 because the sum of the digits gives a number
that can be divided by 3
1 + 4 + 3 + 6 + 1 = 15
15 divided by 3 = 5
99,764
No remainder
Divisible by 4 because the last two digits together
can be divided by 4
64 divided by 4 = 16
No remainder
37,995
Divisible by 5 because the number ends in 5
29,742
Divisible by 6 because the number is divisible by both 2 & 3
2 + 9 + 7 + 4 + 2 = 24
24 divided by 3 = 8
No remainder
• A number divisible by 9 is automatically divisible by 3 also, but
the opposite is not always true
• A number divisible by 8 is automatically divisible by 4 and by
2, but the opposite is not always true
• A number divisible by 4 is automatically divisible by 2, but the
opposite is not always true
• A number divisible by 10 is automatically divisible by 5, but
the opposite is not always true
• If the sum of the digits gives a large number when checking if
a number is divisible by 3, continue adding the digits:
Ex:
29,742
57,819,564
2 + 9 + 7 + 4 + 2 = 24
5 + 7 + 8 + 1 + 9 + 5 + 6 + 4 = 45
2+4=6
6 divided by 3 = 2
4+5=9
9 divided by 3 = 3
A Memory Game
You must know ALL Divisibility Rules
• There are two decks of cards:
• One deck includes Divisibility Rule definitions
• The other includes Phrases that match the definitions
• Play in groups of two
• Place all cards over your desk, facing down
• Oldest person goes first:
• Flip one card from each deck without moving them from
their position
• If the Phrase matches the Divisibility Rule definition:
Keep the cards and continue with your turn
• If the cards don’t match: Put them back face down and
let the other player continue
• Play until all cards have been taken
Player with the most card pairs WINS!