Operations & Algebraic Thinking
Factors & Multiples
Finding factor pairs and recognizing multiples of a number.
Factors and Multiples
Every whole number has a special relationship with the numbers that divide evenly into it, and with the numbers it divides evenly into. Factors and multiples describe those two related but different relationships.
Definition — Factor and Multiple
To find all the factor pairs of a number, test each whole number starting from 1, checking whether it divides evenly. To list multiples of a number, multiply it by 1, 2, 3, and so on — multiples of a number never stop, since there's no largest whole number to multiply by.
Worked Example — Finding All Factor Pairs
Worked Example — Listing the First Several Multiples
Tip
Common Mistakes
Confusing factors and multiples, such as calling 12 a factor of 4 instead of a multiple of 4.
Factors are smaller than or equal to the original number and divide into it evenly; multiples are the same size or larger, produced by multiplying the number.
Stopping the search for factor pairs too early, missing pairs where both numbers are close together, like forgetting 3 × 6 = 18 while only checking 1 × 18 and 2 × 9.
Test every whole number in order starting from 1, and stop only once the two numbers in a pair start repeating the pairs already found in reverse order.
Key Takeaways
- A factor of a number divides evenly into it with no remainder.
- A multiple of a number is the result of multiplying it by a whole number, and multiples never stop.
- Testing whole numbers in order from 1 finds every factor pair of a number.
Summary
Factors and multiples describe how whole numbers relate to each other through multiplication and division. The next lesson uses a similar kind of structured thinking to generate and describe number patterns.
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