What is a factor of a positive integer in this lesson?

Conditions

• The target is a positive integer.
• Only positive integer divisors are considered.

Reasoning, step by step

1. Identify the target positive integer.
2. Find positive integers that divide the target exactly.
3. Verify that pairs of these integers multiply to the target.

Example

For the target 12, the factor pairs are $1\times12$, $2\times6$, and $3\times4$. The complete set of positive factors is $\{1, 2, 3, 4, 6, 12\}$.

Common misconceptions

• Believing a number only has two factors based on seeing a single multiplication pair like $3\times4=12$.
• Including zero or negative integers as factors in this context.

Watch the explanation

Explore next

• What are trivial factors?
• How do I find all the factors of a number like 12?