Use divisibility rules for 2, 3, 4, 5, 6, 8 and 10 times tables to solve problems | Maths

Starter quiz

Match the divisibility rules.
- The number is divisible by 4
  
  ⇔
  
  if halving it gives an even value. ✓
- The number is divisible by 6
  
  ⇔
  
  if it is divisible by both 2 and 3 ✓
- The number is divisible by 8
  
  ⇔
  
  if halving a number twice gives an even value. ✓
- The number is divisible by 3
  
  ⇔
  
  if the sum of the digits is divisible by 3 ✓
Which statements are true?
- 18 is divisible by 3 ✓
- 18 is divisible by 4
- 18 is divisible by 6 ✓
- 18 is divisible by 8
Which statements are not true?
- 30 is divisible by 3
- 30 is divisible by 4 ✓
- 30 is divisible by 6
- 30 is divisible by 8 ✓
True or false? 90 is divisible by 6
- True ✓
- False
Which statements are true?
- 125 is divisible by 3
- 700 is divisible by 8
- 600 is divisible by 4 ✓
- 54 is divisible by 6 ✓
True or false. 48 is divisible by 3, 4, 6 and 8
- True ✓
- False

Match the divisibility rules
- Divisible by 2
  
  ⇔
  
  the ones digit is even ✓
- Divisible by 5
  
  ⇔
  
  the ones digit is 5 or 0 ✓
- Divisible by 10
  
  ⇔
  
  the ones digit is 0 ✓
- Divisible by 9
  
  ⇔
  
  the sum of the digits is divisible by 9 ✓
Which statements are true?
- 30 is divisible by 3 ✓
- 30 is divisible by 6 ✓
- 30 is divisible by 9
- 30 is divisible by 5 ✓
- 30 is divisible by 4
Which statements are not true?
- 60 is divisible by 2 and 4
- 45 is divisible by 9 and 6 ✓
- 40 is divisible by 4 and 10
- 72 is divisible by 8 and 5 ✓
True or false. 198 is divisible by 9
- True ✓
- False
There are 228 competitors at a sports event. They are put into an equal number of teams. How many teams could there be?
- 3 ✓
- 4 ✓
- 8
If there are 390 books in the library and they are organised equally onto shelves, how many shelves could there be?
- 10 ✓
- 9
- 8
- 6 ✓
- 5 ✓

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There are divisibility rules for 2, 4 and 8 which involve halving, halving twice and halving three times.
Multiples of 10 have a zero in the ones and multiples of 5 have a 5 or a zero in the ones.
Multiples of 3 have a digit sum of 3
Multiples of 6 are even numbered multiples of 3

Pupils may struggle to apply multiple divisibility rules simultaneously.

Have the rules visible, practise applying multiple rules step-by-step to ensure understanding and accuracy.

Divisible - divisibility is a number’s ability to be exactly divided by another number, leaving no remainder.
Divisibility rules - divisibility rules let you test if one number is divisible by another, without having to do too much calculation.