Multiplying and dividing by two digits; divisibility · Usually met around P4
Divisibility rules for 2, 3, 5 and 10
2, 5, 10: the last digit. 3: the digit sum.
How to do it
Method
2, 5, 10: the last digit. 3: the digit sum
2457: 2 + 4 + 5 + 7 = 18, so divisible by 3
Another way
Divide to check
2457 ÷ 3 = 819, no remainder
In full
If one number divided by another leaves no remainder, it is divisible by it. You don't need to divide, just look at the digits. A number ending in 0, 2, 4, 6 or 8 is divisible by 2: these are the even numbers, and the rest are odd. A number ending in 0 or 5 is divisible by 5. A number ending in 0 is divisible by 10, and so by both 2 and 5. For 3, add up the digits: 2457 gives 2 + 4 + 5 + 7 = 18, and 18 is divisible by 3, so 2457 is too. Or divide once to check: 2457 ÷ 3 = 819, no remainder.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
8353 is an even number.
True or false?
Show the answer and working
Answer: False
Look at the last digit, 3: a number ending in 0, 2, 4, 6 or 8 is divisible by 2 and even; any other is odd.
Example 2
The three-digit number 72□ is divisible by 3. What is the smallest digit □ can be?
Show the answer and working
Answer: 0
7 + 2 + □ must be divisible by 3: trying □ from 0, the smallest is 0 (digit sum 9).
Example 3
From 1 to 151, □ numbers are divisible by 3 and □ are divisible by 5.
Fill in each box
Show the answer and working
Answer: 50，30
Those divisible by 3 are its multiples: 151 ÷ 3 gives 50. Likewise 151 ÷ 5 gives 30.
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