Divisibility
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Summary
Integer properties are a high-priority ACT topic, especially the relationship among factors, divisors, and divisibility. Mastering these terms, understanding what happens when division is not exact, and using factor pairs systematically will make common number-property questions much easier.
- Integers include positive whole numbers, 0, and negative whole numbers, although most questions here focus on positive integers.
- If a × b = c, then a and b are factors of c; the same relationship can also be expressed by saying a is a divisor of c or that c is divisible by a.
- Factor, divisor, and divisible communicate the same mathematical idea, so ACT questions may switch among these terms without changing the meaning.
- When one integer does not divide another evenly, division can be written either with a quotient and remainder or as a fraction/decimal, and the question will indicate which form matters.
- To find all positive factors of a number such as 36, list factor pairs in order until the pairs repeat or meet in the middle; this guarantees a complete count of the factors.
- Negative factors also exist, but they usually matter less because they mirror the positive factors and appear mainly in more advanced cases.
Chapters
00:00
Understanding Integers and Why They Matter
01:09
Factors, Divisors, and Divisibility
03:56
Handling Division That Is Not Even
05:36
Finding and Counting Factors with Factor Pairs
07:48
Negative Factors and Final Takeaways