Download Divisibility rules

Divisibility rules
“Divisible by”
From Lessons 1-4, we learned that number is “divisible
by” another number when there is no remainder.
Example: 21 is divisible by 7 (21 ÷ 7 = 3)
48 is divisible by 4 (48 ÷ 4 = 12)
24 is not divisible by 5 (24 ÷ 5 = 4 r 4)
33 is not divisible by 2 (33 ÷ 2 = 16 r 1)
Calculator Test
 One way to determine if a number is divisible by
another is to use a calculator.
If the division gives results in a decimal, it is not
divisible by that number
 Example: Look at these two calculations; which is
not divisible by 2?
341 ÷ 2 = 170.5
248 ÷ 2 = 124
Calculator Test continued
 341 ÷ 2 = 170.5
341 is not divisible by 2
(The quotient has a decimal, 170.5)
------------------------------------------------------------- 248 ÷ 2 = 124
248 is divisible by 2
(The quotient has no decimal, 124)
Divisibility Rules
How can you know that a number is
divisible by 2 without actually
doing the division?
Divisibility Rules
 How can you know that a number is divisible by 2
without actually doing the division?
Numbers that end in 0, 2, 4, 6,
or 8 are divisible by 2.
Examples: 20, 14, 436, 208
Divisibility Rules
Can you tell whether a number is
divisible by 10 without dividing?
Divisibility Rules
Can you tell whether a number is divisible by
10 without dividing?
Yes, numbers that end in zero are
divisible by 10.
examples: 20, 100, 250, 1030
Divisibility Rules
Can you tell whether a number is
divisible by 3 without dividing?
Divisibility Rules
Can you tell whether a number is divisible by 3
without dividing?
Yes, but first you must know about
DIGITAL SUMS.
Digital Sums
What is a DIGITAL SUM?
Examples:
The digital sum of 348 is 15. (3+4+8=15)
The digital sum of 1,045 is 10. (1+0+4+5=10)
The digital sum of 111 is 3. (1+1+1=3)
The digital sum of 712,004 is 14 (7+1+2+0+0+4=14)
Divisibility Rules
Can you tell whether a number is divisible by 3
without dividing?
Yes, if the digital sum is divisible
by 3, so is the number.
201 is divisible by 3:
(2+0+1=3 and 3÷3=1 )
Divisible by 3
EXAMPLES:
123 is divisible by 3:
The Digital Sum of 123 is 6 (1+2+3=6)
6÷3=2
452 is not divisible by 3
The Digital Sum of 452 is 11 (4+5+2=11)
11 ÷ 3 = 3r2
Divisibility RAP
 http://www.youtube.com/watch?v=GqulDDVocLo&
NR=1
DIGITAL SUMS
DIGITAL SUMS also works for
numbers divisible by 9.
Digital Sums and 9s
Examples
603 is divisible by 9:
The Digital Sum of 603 is 9 (6+0+3=9)
9÷9=1
459 is divisible by 9
The Digital Sum of 459 is 18 (4+5+9=18)
18 ÷ 9 = 2
Digit Sums
Is 936 divisible by both 3 and 9?
Digit Sums
Is 936 divisible by both 3 and 9?
Digital Sum of 936 is 18.
18 ÷ 3 = 6
18 ÷ 9 = = 2
Yes, 936 is divisible by both 3 and 9.
Digit Sums
Is 444 divisible by both 3 and 9?
Digit Sums
Is 444 divisible by both 3 and 9?
Digital Sum of 444 is 12.
12 ÷ 3 = 4
12 ÷ 9 = = 1r3
No, 444 is divisible by 3 (but not 9).
Video segment #2
Digital Sums song
http://www.youtube.com/watch?v=1ffvCtNZN9Q
One more 3 and 9 explanation:
http://www.youtube.com/watch?v=_-IbZ5Ih_nU
Divisibility Test for 5
How can you tell if these numbers are
divisible by 5?
20; 35; 70; 100; 25; 109,005
Divisibility Test for 5
How can you tell if these numbers are
divisible by 5?
20; 35; 70; 100; 25; 109,005
The last digit is always a 0 or 5.
Divisibility Test for 6
702 is divisible by 6. Why?
It is an EVEN number and the DIGIT SUM is divisible
by 3.
702 is EVEN
7+0+2=9 (9÷3=3)
Divisibility Test for 6
501 is NOT divisible by 6. Why?
BOTH of these MUST BE TRUE:
 EVEN
 Digit Sum is divisible by 3
501 is ODD
5+0+1=6 (6÷3=2)
Divisibility Test for 4
Ignore all digits except for the last two:
432,712
432,712
12 ÷ 4 = 3
----------------------------------------------------------------1324
1324
24÷4=6