#### You may also like Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself! ### Counting Factors

Is there an efficient way to work out how many factors a large number has? ### Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

# Square Routes

##### Age 11 to 14Challenge Level

1. How many 4 digit squares are composed of even numerals?
These square numbers must be between 2000 and 8888 which means that they are squares of numbers between 45 and 94. Moreover the units digit is even. Ong Xing Cong found the following solutions:

68 x 68 = 4624

78 x 78 = 6084

80 x 80 = 6400

92 x 92 = 8464

2. What 4 digit square when reversed becomes the square of another number and why?