Factors, multiples and primes: online calculators

A prime factorisation calculator:

http://www.mathwarehouse.com/arithmetic/numbers/prime-number/prime-factorization-calculator.php

Murderous Maths has an HCF/LCM calculator:

http://www.murderousmaths.co.uk/books/bkmm4xlc.htm

Super-fast addition

Ask the class for two numbers, for example 3 and 5, and use these to generate 10 terms of a Fibonacci-esque sequence:

3, 5, 8, 13, 21, 34, 55, 89, 144, 233

Ask someone to add these up with a calculator while you add them up in your head.

What is the quick way to do this?

Multiplication tricks, part one of many

Squaring a two-digit number ending in 5

The last two digits will always be 25.

To get the first digit(s), take the tens digit of your number and multiply it by the next integer.

Example: 45²

To get the first two digits, multiply 4 by 5 (the next consecutive integer) to get 20. Last two digits are 25. So

45² = 2025.

1089

Via Cut-The-Knot, a magic trick from David Acheson:

http://www.cut-the-knot.org/Curriculum/Arithmetic/S1089.shtml

• Take a three digit number (e.g. 602).
• Reverse it to get another three digit number: 206.
• Subtract the smaller from the larger: 602 - 206 = 396.
• Reverse this number, and add it to the answer obtained: 693 + 396 = 1089.
• Now try with another three digit number. What do you notice?

and a couple of follow-up questions:

• Can you explain it?
• Are there any numbers for which it doesn't work? Why not?