Properties of Integers (Divisors and Multiples)

Listing divisors and multiples comes first, and pulling out what two numbers share leads on to common divisors, the greatest common divisor, common multiples and the least common multiple. Both listing and calculation are covered, along with word problems that ask when a quantity divides evenly and when two cycles line up again.

The most frequent error is choosing the wrong tool for the situation, a greatest common divisor where a least common multiple was needed or the reverse. An answer smaller than the original numbers means a common divisor situation, and a larger one means common multiples. When listing divisors, 1 and the number itself also go missing.

The rows of the times table become a clue for studying number properties from an angle not tried before. What this rests on is the sequence of the 4s and 3s tables memorized in Times Tables: 5, 2, 3, and 4 in grade 2. The numbers found here are used exactly as they are in the unit that follows, Properties of Fractions, for reducing and finding common denominators.