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Free Multiplication Arithmagon Generator – Printable Number Triangle Puzzles

Create printable multiplication arithmagon worksheets in seconds. Choose "factors given", "products given", or mixed difficulty and download ready-to-use PDFs for your math lessons.

CREATE YOUR MULTIPLICATION ARITHMAGON

A multiplication arithmagon is a triangle puzzle where the factors are placed at its vertices and their products are written on the edges between them.

Create printable multiplication arithmagon puzzles

Include solution page
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What are Multiplication Arithmagons?

A multiplication arithmagon is a triangle puzzle with factors at its vertices and their products written on the edges between them. There are three types of puzzle:

  • Factors given. The easiest type. The numbers at the vertices are shown — multiply any two to find the product on the connecting edge.
  • Products given. The most challenging type. The products on the edges are given and you must work backwards to find the factors at the vertices.
  • Mixed. A middle-ground challenge: two products on the edges and one factor at a vertex are revealed. Find the rest.

How to Solve a Multiplication Arithmagon

The Arithmagon

A triangle with factors on the corners and products on the sides.

a b c ab ca bc

1. All Products Given

Given: ab, bc, ca
Find: a, b, c

  1. Multiply all three products together.
  2. Take the square root to get a × b × c.
  3. Divide by each edge product to find each factor.
a= ab·cabc b= ab·bcca c= bc·caab

2. All Factors Given

Given: a, b, c
Find: ab, bc, ca

  1. Multiply adjacent factors.
  2. Repeat for all three sides.
ab=a×b bc=b×c ca=c×a

3. Mixed Information

Given: Some values

  1. Use a known product and a known factor to find a missing factor by dividing.
  2. Fill in values step-by-step.
  3. Use completed edges to solve the remaining sides.
  4. Check consistency by verifying all three products.

How to Use Multiplication Arithmagons in the Classroom

Use as a warm-up: Start your lesson with a quick arithmagon to activate multiplication recall. "Factors given" works best for fast starters.

Differentiate difficulty:

  • Factors given: Multiply corner numbers to find the edge values.
  • Products given: Work backwards from edge values to find the corner numbers.

Choose the right level:

  • Beginners: Factors given
  • Intermediate: Mixed
  • Advanced: Products given

Encourage problem-solving: Ask students to explain their steps, especially for "Products given" puzzles where reasoning and division skills matter.

Use for independent or group work: Students can solve individually, compare answers in pairs, or explain strategies to the class.

Provide immediate feedback: Include a solution page in the worksheet to allow quick checking and self-correction.

More Arithmagon & Multiplication Puzzles

  • Addition Arithmagon Maker
    The same triangle puzzle format using addition instead of multiplication.
  • Multiplication Maze
    Navigate a printable maze by solving multiplication problems along the correct path.
  • Multiplication Product Search
    Find hidden multiplication products in a number grid — a word-search style activity for times-table practice.
  • Multiplication Squares
    Fill in a grid where each cell is the product of its row and column numbers — printable and customizable.

FAQ for Multiplication Arithmagons

What is the difference between factors given and products given?

 Factors given means you multiply the corner numbers to find the edge values — the straightforward direction. Products given means you work backwards from the edge values to find the corner numbers, which requires dividing and taking square roots.

Which multiplication arithmagon type is best for beginners?

 Factors given is the easiest: just multiply each pair of corner numbers to get the edge values. Mixed is intermediate. Products given is the most challenging and requires strong multiplication and division skills.