7. Definition of Divisibility
Divisibility refers to a number's quality of being
evenly divided by another number, without a
remainder left over.
For example:
63 ÷ 7 = 9
50 ÷ 10 = 5
Non examples:
79 ÷ 7 = 11 R2
39 ÷ 9 = 4 R3
8. Why should you learn divisibility?
Divisibility rules of whole numbers are very useful
because they help us to quickly determine if a
number can be divided by single digit numbers and
10 without doing long division. This is especially useful
when the numbers are large.
9. Divisibility Rule for 2
All even numbers are divisible by 2. So, all numbers
ending in 0,2,4,6 or 8 can be divided by 2.
Example: 34,290
Is 1827 divisible by 2?
10. Divisibility Rule for 3
Add up all the digits in the number to find out what
the sum is. If the sum can be divided by 3, the whole
number can be.
Example: 333 (3 + 3 + 3 = 9) and 9 is divisible by 3, so
the whole number is!
Is 3561 divisible by 3?
11. Divisibility Rule for 4
Are the last two digits in your number divisible by 4?
If so, the whole number is too!
Example: 728 (28 is divisible by 4) so the whole
number is!
Is 4876 divisible by 4?
12. Divisibility Rule for 5
Any number ending in a 5 or a 0 are always divisible
by 5.
Example: 1,224,325
Is 0 divisible by 5?
13. Divisibility Rule for 6
If the number is divisible by 2 and 3 it is divisible by 6.
Example: 612 (it is an even number, so it is divisible
by 2) and 6 + 2 + 1 = 9 and 9 is divisible by 3.
Is 108 divisible by 6?
14. Divisibility Rule for 7
If you double the last digit and subtract it from the
rest of the number and the answer is:
0 OR divisible by 7.
Example: 672 (Double 2 is 4, then 67-4=63, and 63 is
divisible by 7.)
Is 2457 divisible by 7?
15. Divisibility Rule for 8
If the last 3 digits are divisible by 8.
Example: 1824 (824 is divisible by 8)
Is 4120 divisible by 8?
16. Divisibility Rule for 9
If the sum of the digits is divisible by 9, then the
whole number is divisible by 9.
Example: 999 (9 + 9 + 9 = 27) and 27 is divisible by 9,
so the whole number is.
Is 5364 divisible by 9?
18. Answer
Yes No No No Yes No No
Yes No Yes No Yes No No Yes
Yes No Yes No No Yes Yes No
Yes Yes Yes No Yes No Yes Yes
No No No No No No No
Yes Yes Yes No Yes Yes No Yes
Yes No Yes Yes No No Yes No
Yes No Yes Yes No No Yes No
No Yes No No No No No
Let’s try filling out
this chart using
divisibility rules
19. Divisibility Rule for 10
If a number ends in a 0, it is divisible by 10. Also if a
number is divisible by both 2 and 5, it is divisible by
10
Example: 30, 55800, 67920
24. Practice Problem:
There are 1,728 fish in a hatchery, which are divided
evenly among the ponds. How many ponds could
there be at the hatchery?
a)10
b)4
c)5
25. Answer
There are 1,728 fish in a hatchery, which are divided
evenly among the ponds. How many ponds could
there be at the hatchery?
b) 4
27. Answer
If we can verify that 41295 is divisible by both 3 and 5, then it is
divisible by 15.
Sum of the digits in 41295 : 4 + 1 + 2 + 9 + 5 = 21
Because 21 is a multiple of 3, 41295 is divisible by 3.
In 41295, the digit in one's place is 5.
Therefore, 41295 is divisible by 5.
Now, it is clear that 41295 is divisible by both 3 and 5. So, 41295 is
divisible by 15.
32. Time for handouts!
Take the handouts that you printed out at home and using the
concepts that we learned today, start working on them. If you don’t
finish that’s okay, you can finish it at home.