**Divisibility Rules of whether a number is divisible by 2, 3, 4, 5, 6, 8, 9 and 10**

Number | Rule | Example |
---|---|---|

2 | Last digit in the number is even. | 14, 102, 118, 560 all end in even numbers, so all are divisible by 2. |

3 | Sum of the digits of the number is divisible by 3. | The sum of the digits of 396 is 3+9+6 = 18 which is divisible by 3, so 396 is divisible by 3. |

4 | Number formed by the last 2 digits is divisible by 4. | Last 2 digits of 1424 is 24, which is divisible by 4, so 1424 is divisible by 4. |

5 | Last digit is 0 or 5 | 35, 90, 475 |

6 | Number is even and divisible by 3. | 144 is even and is divisible by 3 (sum of digits 1+4+4 = 9, divisible by 3), so 144 is divisible by 6. |

8 | Last 3 digits divisible by 8 or Last 3 digit is 000 | Last 3 digits of 83400 is 400 which is divisible by 8. Last 3 digits of 1000 is 000 hence it is divisible by 8 |

9 | Sum of the digits of the number is divisible by 9. | Sum of the digits of 1485 is 1+4+8+5 = 18 which is divisible by 9, so 1485 is divisible by 9 |

10 | Last digit is 0 | 90, 120, 680 |

**Number Divisibility Rules**

## Problems on Divisibility

**1. Determine the following numbers which are divisible by 2, using the test of divisibility by 2:**

(i) 176, (ii) 221, (iii) 327, (iv) 90, (v) 192

**2. Let us consider the following numbers to find whether the numbers are divisible or not divisible by 3:**

(i) 176, (ii) 221, (iii) 327, (iv) 90, (v) 192

**3. Is 7248 is divisible (i) by 4, (ii) by 2 and (iii) by 8?**

**4. Without actual division, find if 235932 is divisible (i) by 4 and (ii) 8.**

**5. Determine which of the following numbers which are divisible by 6, using the test of divisibility by 6: 42, 144, 180, 258, 156**

**6. Determine which of the following numbers which are divisible by 9, using the test of divisibility by 9: **

99, 198, 171, 9990, 3411.