Number Blocks Tool
Type a whole number from 0 to 999,999,999. The tool splits it into place-value blocks, says whether it is odd or even, checks whether it is prime, lists its factors, and builds a practice card you can print. Everything is worked out in your browser; nothing is sent anywhere.
36 broken down
Place value
| Place | Digit | Worth |
|---|---|---|
| tens | 3 | 30 |
| ones | 6 | 6 |
Expanded form: 30 + 6
Number facts
- Even: 36 makes 18 pairs with none left over.
- Composite: it has more than two factors.
- Square number: 6 × 6.
- Triangular number: 1 + 2 + … + 8 = 36.
- Digit sum: 9, so it is a multiple of 3 and of 9.
Factors and prime factors
Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factor pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
Prime factorization: 2² × 3²
Block picture
Each small square is one. A column is a ten, a flat square is a hundred. Larger places are shown as labelled stacks so the picture stays readable.
Rectangles you can build
A number that can be laid out as a rectangle with at least two rows and two columns is composite. A prime number only makes a single line.
Practice card for 36
- How many tens are in 36? ____
- Write 36 in expanded form. ____________
- Is 36 odd or even? How do you know? ____________
- Is 36 prime or composite? ____________
- Write two factor pairs of 36. ____________
- What is 36 + 10? ____ What is 36 - 10? ____
Answers
Answers
- 3 tens (and 6 ones).
- 30 + 6
- Even: it ends in 6, so it splits into two equal groups of 18.
- Composite: 36 has 9 factors.
- Any two of 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.
- 46 and 26.
numblocksgen.com/number-blocks-tool/
How to read the results
Place value tells you what each digit is worth. In 4,507 the 5 is worth five hundred, while the 0 holds the tens place open so the 4 can stay in the thousands. The table lists every place, including zeros, because a missing zero is one of the most common reasons a child writes 457 when they mean 4,507.
Odd or even is decided by the ones digit alone. If you can share the number into two equal groups with nothing left over, it is even; the tool also shows the size of each group.
Prime or composite: a prime has exactly two factors, 1 and itself. Zero and one are neither. For composite numbers the tool lists every factor pair (for numbers up to ten million) and the prime factorization, which is the same no matter which factor pair you start from.
Rectangles are a picture of multiplication. 12 blocks can be arranged as 2 × 6 or 3 × 4; 13 blocks only make a 1 × 13 line. The tool draws the rectangles for numbers up to 144 so the grid stays clear on a phone screen.
Ideas for using it at home or in class
- Guess first, then check. Before pressing the button, ask "Do you think 51 is prime?" Many people say yes; the tool shows 3 × 17.
- Hunt for patterns. Try 9, 99 and 999, or 10, 100 and 1,000, and talk about what changes in the place-value table.
- Build it for real. Use Lego, snap cubes or coins to copy the block picture, then rebuild it as one of the rectangles.
- Print a card a day. Use a different number each morning; the answers are on the card so an older sibling or the learner can mark it.
- Connect it to the generator. In the Number Blocks Generator, press Break it down or open Number facts to jump here with the number that is on screen.