Egyptian multiplication methods did not require a great deal of memorization, just a knowledge of the two times tables. For a simple example, to multiply 12 times 16, they would start with 1 and 12. Then they would double each number in each row (1 × 2 and 12 × 2; 2 × 2 and 24 × 2; and so on) until the number 16, resulting in the answer 192:

1 |
12 |

2 |
24 |

4 |
48 |

8 |
96 |

16 |
192 |

Another example computes a number that is not a multiple in the row, such as 37 times 19:

1 |
19 |

2 |
38 |

4 |
76 |

8 |
152 |

16 |
304 |

32 |
608 |

First, do the usual procedure by starting with 1 and 19, then doubling the numbers until you get to 32 (if you double 32 [_ 64], you’ve overshot the number 37). Because 37 is higher than 32, go back over the list on the left hand side, figure out which numbers, with 32, add up to 37 (1, 4, and 32); then add the numbers that correspond to those numbers, to the right (19, 76, and 608), which equals the answer: 703. And you didn’t even need a calculator!