Math 81
Activity # ____
“Tests for Divisibility”
Your Name: ___________________ Team Member #1__________________
Team Member #2.______________ Team Member #3__________________
The Fundamental Theorem of Arithmetic- Any whole number greater than 1 is
either Prime or may uniquely be expressed as the product of positive prime numbers.
This theorem tells us that we may break down “composite numbers” into unique prime
number factor representations. A great aid in performing this task is the “Tests for
Divisibility”. If a whole number can be divided by another whole number leaving no
remainder (remainder is 0) we say that the first number is “divisible” by the second
number. Or that the second number will divide the first.
Tests for Divisibility:
1) Any whole number is divisible by 2 if it is even. A number is called even if the
last digit or unit’s digit is 0, 2,4,6,8.
2) Any whole number is divisible by 3 if the sum of the digits is divisible by 3.
Example: 351is divisible by 3 because 3  5  1  9 and 9  3  3.
3) Any whole number is divisible by 5 if the last digit or unit’s digit is 0 or 5.
4) Any whole number is divisible by 10 if the last digit or unit’s digit is 0.
Task 1: For each of the following whole numbers determine whether it’s divisible by
2, 3, 5, and 10 and explain why it’s divisible.
Example: 420
Note: You may just write the reason given in parentheses.
a) 2 will divide 420 since it is an even number (even number)
b) 3 will divide 420 since 4+2+0 = 6, and 6÷3 = 2 (sum of the digits is divisible by 3)
c) 5 will divide 420 since the last digit is 0 (ends in 0)
d) 10 will divide 420 since the last digit is 0 (ends in 0)
1
1) 225
Reasons:
2) 111
Reasons:
3) 123,960
Reasons:
4) 480
Reasons:
5) 45,000
Reasons:
6)
578,400
Reasons:
Here are a couple less common Tests for Divisibility:
1) Any whole number is divisible by 4 if the last two digits of the whole number
form a number that is divisible by 4.
Example: 372 is divisible by 4 because 72 is the last two digits and 72  4  18 .
Note: that 00 is considered to be divisible by 4.
Example: 200 is divisible by 4 because 00 is the last two digits and 00  4  0 .
(Note: 200  4  50 )
2) Any whole number is divisible by 9 if the sum of the digits is divisible by 9.
Similar to 3.
Example: 567 is divisible by 9 because 5  6  7  18 and 18  9  2.
2
Task 2: For each of the following whole numbers list whether 2, 3,4,5,9 or 10 will
divide them and then explain why.
Example: 936
Note: You may just write the reason given in parentheses.
a) 2 will divide 936 since it is an even number. (even number)
b) 3 will divide 936 since 9+3+6=18 and 18 ÷ 3 =6 (sum of the digits is divisible by 3)
c) 4 will divide 936 since 36 ÷ 4 = 9 (last two digits form a number divisible by 4)
d) 9 will divide 936 since 9+3+6=18 and 18 ÷ 9 =2 (sum of digits divisible by 9)
1) 372
Reason:
2) 45,000
Reason:
3) 632,448
Reason:
4) 6930
Reason:
5) 117,000
Reason:
6) 18000
Reason:
3