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Worksheet 1: Divisibility Rules, Multiples, Factors
Divisibility Rules
The divisibility rules help you to find factors.
A number is divisible by:
2 if it ends with an even number (0, 2, 4, 6, or 8)
3 if the sum (add up all the digits) of the digits is divisible by 3.
4 if the last two digits are divisible by 4
5 if it ends in 0 or 5
6 if it is divisible by 2 and 3
8 if the last three digits are divisible by 8
9 if the sum (add all the digits) of the digits is divisible by 9
10 if it ends in 0
1. Complete the chart
Number
Is it
divisible
by 2?
How do
you
know?
Is it
divisible
by 3?
How do
you
know?
Is it
divisible
by 4?
How do
you
know?
Is it
divisible
by 5?
How do
you
know?
Is it
divisible
by 6?
How do
you
know?
Is it
Is it divisible by 9?
divisible How do you know?
by 8?
How do
you
know?
1422
3456
37185
564285
307462288
Multiples
2. Write the next 4 multiples for each number.
a.
5 _______ _______ ________
________
b.
8
_______ _______ ________
________
c.
20 _______ _______ ________
________
d.
20 _______ _______ ________
________
e.
25 _______ _______ ________
________
Just count by the number
or multiply it first by “2”,
then by “3” then by
“4”….
Extension
d.
79 _______ _______ ________
________
Remember
divisibility
rules!!
2. Circle the numbers which are multiples of the bold numbers:
a. 5
12
10
345
b. 3
6
9
34
5
20
17
478
98765
12
20
c. 2
4
29
45
4
8
45432
d. 8
16
24
90
80
248
9876800
e. 10
30
45
78
40
20
10000000
3. Record multiples for each, circle common multiples and indicate Lowest Common Multiple (LCM)
Multiples of 8
___ ____ ____ ____ ____
____
____ ____
Multiplies of 6
___ ____ ____ ____ ____ ____
____ ____
LCM______
4. Record multiples for each, circle common multiples and indicate Lowest Common Multiple (LCM)
Multiples of 9
___ ____ ____ ____ ____ ____
____ ____
Multiples of 5
___ ____ ____ ____ ____
____ ____
LCM______
____
3. Extension:
Multiples of 60
Multiples of 159
___ ____ ____ ____ ____
___ ____ ____ ____ ____
____
____
____ ____
____ ____
LCM______
Factors
Write the factors for each number. Then list the common factors (CF) (factors that show up in both lists)
and the greatest common factor (GCF)( the biggest number in the group of the common factors).
4.
12
15
Common Factors (CF) are:____________________________
Greatest Common Factor (GCF) is ______
5.
25
50
Common Factors (CF) are:____________________________
Greatest Common Factor (GCF) is ______
6.
48
36
Common Factors (CF) are:____________________________
Greatest Common Factor (GCF) is ______
Extension:
7.
Find CFs and GCF for 408 & 510
8. Find CFs and GCF for 438 & 192
9. Find LCM and GCF of
98, 55, 64
(you could use prime factorization)
Puzzles for you to enjoy (or not).
1. MOVING HOLE:
By cutting this square piece of paper into two and only two pieces (and rearranging those pieces),
how is it possible to move the hole into the center of the square?
2.
CONNECT THE DOTS:
How many squares can you create in this figure by connecting any 4 dots (the corners of a square
must lie upon a grid dot).