Is there an efficient way to work out how many factors a large number has?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Suppose you had to begin the never ending task of writing out
the natural numbers: 1, 2, 3, 4, 5.... and so on.
What would be the 1000th digit you would write down. In what
number would it occur?
What number would contain the millionth digit?
When would you have written six for the 6000th time?