**2:**All even numbers are divisible by 2. Odd numbers are not divisible by 2.

- Any number that ends in a 0, 2, 4, 6, or 8 is even and can be divided by 2.
- 20, 34, 96, 48, and 102 are all divisible by 2.
- 31, 19, 27, 45, and 103 are not divisible by 2.

**3:**If all the digits in a number add up to 3, 6, or 9, the number is divisible by 3.

- For example, take the number 45. If you add the numbers 4 and 5 you get 9, which is divisible by 3. This means that the number 45 is divisible by 3.
- Another example is 57. If you add 5 and 7 you get 12. Now if you add the 1 and 2, you get 3. This means that the number 57 is divisible by 3.
- One last example is 19. If you add the 1 and 9, you get 10, which is not divisible by 3. This means that the number 19 is not divisible by 3.
- 15, 33, 63, 84, and 105 are all divisible by 3.
- 14, 32, 58, 71, and 103 are not divisible by 3.

**4:**Many (not all) even numbers are divisible by 4. Odd numbers are not divisible by 4.

- 16, 32, 48, 64, and 100 are all divisible by 4.
- 13, 39, 47, 86, and 105 are not divisible by 4.

**5:**Any number that ends in a 0 or 5 is divisible by 5.

- 10, 25, 40, 65, and 115 are all divisible by 5.
- 24, 32, 58, 77, and 112 are not divisible by 5.

**6:**Any number that is divisible by both 2 and 3 is divisible by 6.

(Since odd numbers are not divisible by 2, odd numbers are also not divisible by 6.)

- Ex: 21 is odd, so it is not divisible by 2, so not divisible by 6 (but it is divisible by 3).
- Ex: 24 is even, so it is divisible by 2; 2+4=6, so it is divisible by 3; since 24 is divisible by both 2 and 3, it is divisible by 6.
- 18, 36, 54, 84, and 108 are all divisible by 6.
- 15, 33, 46, 92, and 103 are not divisible by 6.

**7:**Unfortunately, there’s not a good trick for 7, so memorizing the numbers is the best way.

- 7, 14, 21, 28, 35, 42, 48, 56, 63, and 70 are all divisible by 7.
- All other numbers under 70 are not divisible by 7.

**8:**Some (not all) even numbers are divisible by 8. Odd numbers are not divisible by 8.

If the number is not divisible by 4, it will not be divisible by 8.

- 16, 32, 56, 88, and 120 are all divisible by 8.
- 18, 35, 49, 74, and 105 are not divisible by 8.

**9:**If all digits in a number add up to 9, the number is divisible by 9.

- Ex: 27 –> 2+7=9, so this number is divisible by 9.
- Ex: 99 –> 9+9=18 –> 1+8=9, so this number is divisible by 9.
- Ex: 39 –> 3+9=12 –> 1+2=3, so this number is not divisible by 9 (however, it is divisible by 3).
- 36, 45, 72, 81, and 108 are all divisible by 9.
- 24, 55, 68, 93, and 112 are not divisible by 9.

**10:**All numbers that end in 0 are divisible by 10.

- 20, 40, 80, 100, and 130 are all divisible by 10.
- 22, 46, 71, 111, and 118 are not divisible by 10.

Examples – List all the numbers 2 through 10 that can be divided into the following:

## 33

- This number is odd, so it is not divisible by 2, 4, 6, or 8.
- 3+3 = 6, so this is number is divisible by
**3**, but not 9. - This number does not end in a 0 or 5, so it is not divisible by 5 or 10.
- This number is under 70 and not listed in the numbers for 7.
- Answer:
**3**

## 58

- This number is even, so it is divisible by
**2**. - This number is even, so it may be divisible by 4 or 8.
- Check: 58 ÷ 4 does not equal a whole number, so not 4.
- Since it is not divisible by 4, it is also not divisible by 8.

- 5+8 = 13 –> 1+3 = 4, so not divisible by 3 or 9.
- This number is divisible by 2, but not by 3, so it is not divisible by 6.
- This number does not end in a 0 or 5, so it is not divisible by 5 or 10.
- This number is under 70 and not listed in the numbers for 7.
- Answer:
**2**

## 54

- This number is even, so it is divisible by
**2**. - This number is even, so it may be divisible by 4 or 8.
- Check: 54 ÷ 4 does not equal a whole number, so not 4.
- Since it is not divisible by 4, it is also not divisible by 8.

- 5+4 = 9, so it is divisible by both
**3**and**9**. - This number is divisible by 2 and 3, so it is divisible by
**6**. - This number does not end in a 0 or 5, so it is not divisible by 5 or 10.
- This number is under 70 and not listed in the numbers for 7.
- Answer:
**2, 3, 6, 9**

## 35

- This number is odd, so it is not divisible by 2, 4, 6, or 8.
- 3+5 = 8, so this is number is not divisible by 3 or 9.
- This number ends in a 5, so it is divisible by 5.
- This number is under 70 and is listed in the numbers for 7.
- This number does not end in 0, so it is not divisible by 10.
- Answer:
**5, 7**

Practice makes perfect – What numbers 2 through 10 can be divided into the following:

- 45
- 32
- 60
- 39
- 86
- 56

## Comments

1122= 42