Finding the missing factor

Finding the missing factor

Finding the missing factor

Sometimes a multiplication equation has a hole in it:

4 × ? = 28

The challenge is to find the missing factor — the number that fills the hole.

Strategy 1 — count up by the known factor

Skip-count by 4 until you reach 28:

4, 8, 12, 16, 20, 24, 28.

That was 7 jumps. So 4 × 7 = 28.

This works well for small known factors (2, 5, 10).

Strategy 2 — use division

Multiplication and division are opposite operations. The missing factor in `4 × ? = 28` is exactly `28 ÷ 4`:

28 ÷ 4 = 7

So 4 × 7 = 28.

This is faster once you know your tables — every multiplication fact is also a division fact.

Two equations, same family

Every multiplication fact gives you a family of four equations:

4 × 7 = 28

7 × 4 = 28

28 ÷ 4 = 7

28 ÷ 7 = 4

Knowing one gives you all four. The missing factor exercise just hides one of them.

What if the unknown is on the left?

? × 6 = 42

Same idea — divide: 42 ÷ 6 = 7. So 7 × 6 = 42.

Watch out — only multiples appear

The product (right side of `=`) is always a multiple of the known factor. If the equation is `4 × ? = 27`, something is wrong — 27 is not in the 4× table. Real exercises never trick you like that, but it's a useful sanity check.

Try it

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