Factor Forest

Which numbers divide it exactly? And which numbers have no pairs at all?

Book Factors and multiples 4.OA.B.4 ALPACA · Elementary operations ARF · Division facts
▤ Print this All of 4th grade

For grown-ups

  • How long: 10 to 15 minutes is plenty. Short and frequent beats long and occasional — the early-numeracy trials with the largest effects ran eight weeks or less.
  • When they get one wrong: the page shows the working. Read it together rather than moving straight on. Feedback that explains is worth several times more than feedback that only marks right or wrong, and that gap is wider in maths than in any other subject.
  • Not timed: thinking time is the point of a book. Let silences run.
  • Print it too: doing the same problems on paper a few days later is worth more than doing twice as many today.

What this practises

Finding factor pairs, listing multiples, and telling a prime from a composite.

Factors are usually taught as a list to memorise. Presented as rectangle dimensions they become a search with a visible answer — and it explains primes properly: a prime is a number you cannot make into any rectangle except a single row.

The underlying idea
A factor pair is the two sides of a rectangle with that many squares. Primes are the numbers that can only be a single line.
Where this sits in Illustrative Mathematics
4th grade Unit 1: Factors and Multiples
Sources
Illustrative Mathematics / Kendall Hunt (2024) · youcubed et al. (2015) · Fyfe et al. (2014)  all references →

Related measured skills: ALPACA · Elementary operations, ARF · Division facts. What this means