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Break down 144: a dozen squared and a factor playground

This page is a static breakdown of 144 — readable without pressing Play. Use it as a teaching note, then open the live tool to change the number.

Generate rectangles, factors and a fresh printable card for 144. Try 144 in the tool

Why this number

  • 144 is 12 squared, so it sits at the edge of common times-table knowledge.
  • Its prime factorization 2⁴ × 3² produces many rectangles — ideal for the tool view.
  • It is large enough to feel "big" while still fitting on a printed card.

Place value

144 by place
PlaceDigitWorth
hundreds1100
tens440
ones44

Expanded form: 100 + 40 + 4

Odd or even, prime status

  • Even — ones digit 4.
  • Prime status: composite (prime factorization 2⁴ × 3²).
  • Square: yes. Triangular: no.

Factor pairs and rectangles

1 × 144, 2 × 72, 3 × 48, 4 × 36, 6 × 24, 8 × 18, 9 × 16, 12 × 12.

Proper rectangles (both sides > 1): 2 × 72, 3 × 48, 4 × 36, 6 × 24, 8 × 18, 9 × 16, 12 × 12.

Teaching moves

  1. Predict whether 144 is prime (it is not) before opening the tool.
  2. Write 100 + 40 + 4, then confirm in the place-value table.
  3. Challenge: how many factor pairs can you find in two minutes? Check against the tool list.

Practice card for 144

Open full tool

Six questions with answers for 144: place value, expanded form, odd or even, prime or composite, factor pairs, and ±10. Print it, or pick any other number in the Number Blocks Tool.

  1. How many tens are in 144? ____
  2. Write 144 in expanded form. ____________
  3. Is 144 odd or even? How do you know? ____________
  4. Is 144 prime or composite? ____________
  5. Write two factor pairs of 144. ____________
  6. What is 144 + 10? ____ What is 144 - 10? ____
Answers

Answers

  1. 14 tens (and 4 ones).
  2. 100 + 40 + 4
  3. Even: it ends in 4, so it splits into two equal groups of 72.
  4. Composite: 144 has 15 factors.
  5. Any two of 1 × 144, 2 × 72, 3 × 48, 4 × 36, 6 × 24, 8 × 18, 9 × 16, 12 × 12.
  6. 154 and 134.

numblocksgen.com/number-blocks-tool/

Also try the Number Blocks Generator with Set → 144, then Break it down. More cards: place value printable pack.

Related lessons

Prime and composite numbers, shown with rectanglesA visual definition of prime numbers using block rectangles, why 1 is not prime, how to test a number quickly, and the primes below 100.Finding factor pairs with arraysA systematic way to list every factor of a number, how arrays show multiplication, and why square numbers have an odd number of factors.Square and triangular numbers: building shapes from blocksBuild square and triangular numbers with blocks, spot how they grow, and discover how two triangles make a rectangle.

Other example numbers

Break down 36: place value, factors and square shapeA full SSR breakdown of 36: place value, expanded form, factor pairs, rectangles, and why 36 is both square and triangular — with a link to try it in the Number Blocks Tool.Break down 100: one hundred as place value and bondsWhy 100 is a landmark number: one hundred flat of blocks, bonds to 100, and place-value shifts when you add or subtract ten.