3rd grade · 12 facts · division

Dividing by 6

Dividing by 6 is where division starts to depend on memorized multiplication. 42 ÷ 6 = 7 because 6 × 7 = 42, and no halving or counting shortcut beats knowing that fact. The upside is that this page is exactly as hard as the 6 times table: once those facts are known, the division comes with them.

For a child still learning, a helpful route is to divide by 2 and then by 3, because 6 is 2 × 3. For 48 ÷ 6, half of 48 is 24, and 24 ÷ 3 = 8. It is a longer path, but each step uses an easier table.

All 12 divide-by-6 facts

  • 6 ÷ 6 = 1
  • 12 ÷ 6 = 2
  • 18 ÷ 6 = 3
  • 24 ÷ 6 = 4
  • 30 ÷ 6 = 5
  • 36 ÷ 6 = 6
  • 42 ÷ 6 = 7
  • 48 ÷ 6 = 8
  • 54 ÷ 6 = 9
  • 60 ÷ 6 = 10
  • 66 ÷ 6 = 11
  • 72 ÷ 6 = 12

Every fact here divides evenly. Division with remainders comes in 4th grade.

Printable practice sheet (PDF) — 24 problems: the 12 facts in order, then the same facts mixed up. The answer key is on page 2. Free to print, no sign-up.

Timed drill: dividing by 6

12 facts in a random order. A right answer within 3 seconds counts as by heart. Free, no sign-up, and nothing is saved: it all happens on this screen.

Type with the keypad or your keyboard, then press Check or Enter.

What to notice

Every starting number is even and in the 3s. That gives a two-part test: a number divides by 6 with nothing left over only if it is even and its digits add to 3, 6 or 9. 54 is even and 5 + 4 = 9, so 54 ÷ 6 works; 64 is even, but 6 + 4 = 10, so it does not.

The 6s echo works backwards for the even answers. 6 × 4 = 24, 6 × 6 = 36 and 6 × 8 = 48, so the ones digit of the starting number is the answer: 24 ÷ 6 = 4, 36 ÷ 6 = 6, 48 ÷ 6 = 8.

The middle facts are the ones to watch: 36 ÷ 6, 42 ÷ 6 and 48 ÷ 6. They are the same facts children find hardest in the 6 times table.

How to practise at home

  • Practise the matching multiplication fact first. If 6 × 7 is slow, 42 ÷ 6 will be slow too, so spend a few days on the times table.
  • Use an egg carton, which has 6 cups to a row. Share 18 beads along one row, one cup at a time, and count one cup.
  • Ask both questions for each fact: “how many 6s in 54?” and “what times 6 is 54?”
  • Run the drill on this page, note which facts are slow, and practise those as multiplication facts for a few days.
  • Use five-and-one-more backwards: 42 is 35 and 7, which is five 7s and one more 7, so 42 ÷ 6 = 7. Breaking the big number into a 5s answer and one more group helps a child who knows the 5s well.

Slips to watch for

  • Mixing up 42 ÷ 6 and 48 ÷ 6, and answering 8 for 42 ÷ 6. Check with the multiplication: 6 × 8 = 48.
  • Leaning on the test alone. 30 is even and its digits add to 3, so it divides by 6, but your child still needs to know it is five 6s.
  • Answering 0 for 6 ÷ 6. Six shared among six is one each.

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