Teachers in my math workshops like me to share some multiplication and factoring tips I teach my students. These help with number sense as well. I hope they can be useful for you too.

**Tips for Multiplying Whole Numbers**

- Times 2: Double the number. If multiplying by 2, the result will always be even.
- Times 3: Triple the number. Products alternate odd and even (3, 6, 9, 12, etc.).
- Times 4: Double the number twice. The result will always be even.
- Times 5: The result must have a 5 or a 0 in the ones place.
- Times 6: Triple the number and double it, in whichever order is easiest.
- Times 7: These must be memorized. (Please add a comment below if you know a trick for these!)
- Times 8: Double the number once, double it again, and double it a third time. The result will always be even.
- Times 9: Two tricks here for multiplying single digits by 9. 1) The fingers trick: see http://www.multiplication.com/lesson10_nines_fingers.htm.
- 2) Take the number you are multiplying by 9, for example 7. The tens digit will be one less than the multiplier (6, in this example). The ones digit will be whatever it takes for the two digits to add up to 9. In this example, 6 + 3 = 9, so the answer is 63.
- Times 10: The concept here is that when multiplying by 10, it increases by one place value. So 1 x 10 is 10, 10 x 10 is 100, etc. Thus you append a 0 to the number, increases the value by one place. The result will always be even.
- Times 11: For 1-9, the result is always that both digits will be the same as the multiplier, for example, 3 x 11 = 33. For two-digit numbers 10-19, there is a cool trick. The first digit will be the same as the first digit of the multiplier; the second digit will be the two multiplier digits added together; and the last digit will be the second digit of the multiplier. For example: 11 x 18 = 198, 11 x 13 = 143, etc. Just sandwich in the sum of the multiplier’s digits between the multiplier’s digits to get your product!
- Times 12: Same as the 6 trick, but double the result.

**Tips for Dividing or Factoring Whole Numbers**

If you are trying to check to see if a number is divisible by another number, or can be factored by that number, or has a common factor with another number, these tips can be helpful.

- Divisible by 2: Any even number.
- Divisible by 3: Add up the digits as if they are all ones. If the sum is divisible by 3, the number is divisible by 3.
- Examples: 143 -> 1+4+3 -> 8, so not factorable by 3. 144 -> 1+4+4 -> 9, so factorable by 9
- Divisible by 4: If an even number is still even when you cut it in half, it is divisible by 4.
- Divisible by 5: Any number ending in 5 or 0.
- Divisible by 6: Any even number that fits the 3 rule.
- Divisible by 7: Memorize these.
- Divisible by 8: If an even number is still even when you cut it in half, and in half again, it is divisible by 8.
- Divisible by 9: Same as 3 rule, except the sum of the digits must be a multiple of 9.
- Divisible by 10: Any number ending in 0.
- Divisible by 11: See the Times 11 rule and reverse it.
- Divisible by 12: Any number that fits both the 3 rule and the 4 rule.

I also recommend Greg Tang’s book The Best Of Times, which is full of multiplication tricks like these, but in a fun, picture book format that children will enjoy experiencing.

A great video showing how to fill in a times table chart, and learn the facts while you are doing so, can be found here:

http://mathplayground.com/howto_learnmultfacts.html

If you have learners who struggle to learn their multiplication facts because they have trouble memorizing or can’t learn through these tips, or are just kinesthetic learners, try playing games where children toss a ball back and forth while skip counting with different tables. If they don’t know the tables at all, they can use a chart on the wall for reference while they are learning. Like with any skill, practice and repetition will eventually lead to mastery.