## Last Digit of a Product

The last digit of any multiplication depends only on the last digit of each number being multiplied, and not for example, on the size of the numbers or their order.

\[3 \times 2=6\]

If the last digit of a number is 2 and the last digit of any other number is 3, the last digit of their multiple will be 6, so the last digit of

\[53 \times 42=2226\]

is 6. The complete list of posdible combinations of last digits is given in the table.Number A\Number B | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

2 | 0 | 2 | 4 | 6 | 8 | 0 | 2 | 4 | 6 | 8 |

3 | 0 | 3 | 6 | 9 | 2 | 5 | 8 | 1 | 4 | 7 |

4 | 0 | 4 | 8 | 2 | 6 | 0 | 4 | 8 | 2 | 6 |

5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 |

6 | 0 | 6 | 2 | 8 | 4 | 0 | 6 | 2 | 8 | 4 |

7 | 0 | 7 | 4 | 1 | 8 | 5 | 2 | 9 | 6 | 3 |

8 | 0 | 8 | 6 | 4 | 2 | 0 | 8 | 6 | 4 | 2 |

9 | 0 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |