PBCC 1 SLC Lake Worth Math Lab
Divisibility Rules
Which of the following fractions can be written in lowest terms?
i)
117
225 ii) 27
42 iii)
51
85 iv)
128
131
Divisibility rules can be used to determine whether or not a fraction needs to be reduced. The
rules are based on the patterns that occur when we list the multiples of any number. For
example, when we list the multiples of 2, we get even numbers – numbers that end in 0, 2, 4,
6, or 8.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …
This means that all even numbers share a common factor of 2. So if the numerator and the
denominator of a fraction are both even numbers, such as 4/6, we can reduce the fraction by
canceling the common factor of 2:
4222
6233
∗
==
∗
Other divisibility rules are listed below. After you have read the rules, use them to determine
which of the fractions above is written in lowest terms and which can be simplified. Simplify
any fractions that are not written in lowest terms.
Number
0
1
2
3
4
5
Rule
Division by 0 is undefined – for example, 5undefined
0=.
Every number is divisible by 1
If a number ends in 0, 2, 4, 6, or 8 (even), the number is divisible by 2.
If the sum of a number's digits is a multiple of 3, the number is divisible by
3. For example, 3 divides 18. When we add the digits of 18, we get a
multiple of 3. This tell us we can divide the number by 3.
18 → 1 + 8 = 9.
If the last two digits of a number are divisible by 4, the number is divisible
by 4. If the last two digits of a number are 0's, the number is divisible by 4
because 4 divides 100. For example, 324 is divisible by 4 because 4
divides 24, and 1500 is divisible by 4 because the last two digits are 0's.
If a number ends in 0 or 5, the number is divisible by 5.
