New book published

Mathematics Explained for Healthcare Practitioners is now officially published!
Here's the cover:

And here's the link for more details: http://www.uk.sagepub.com/books/Book237689
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In my last post I asked some questions about '2013'.

a) You can tell this is not a prime number because the digits sum to 6, which is a multiple of 3. All numbers which have digital sums that are multiples of 3 are themselves multiples of 3.

b) 2013 ÷ 3 = 671.
Then you can see immediately that 671 is a multiple of 11 because 6 + 1 = 7! (A trick for spotting multiples of 11!)
So, 671 = 61 × 11.
61 and 7 are prime, so we can go no further with factorising.
So 2013 has at least these factors: 1, 3, 11, 61, 671 and 2013. But then we can get other factors by pairing some of these up: for example, 3 × 11 = 33 must be a factor of 2013. So must 3 × 61 = 183.
So altogether we have eight factors: 1, 3, 11, 33, 61, 183, 671 and 2013.

c) There has been an interesting sequence of times during this millennium so far:
8.01 pm on 20th January 2001 was 20:01, 20.01.2001.
Exactly 1 year, 1 month and 1 minute later we got to 20:02, 20.02.2002!
Another 1 year, 1 month and 1 minute later it was 20:03, 20.03.2003!
And so on, up to 20:12, 20.12.2012, last year.
But that's where the sequence stops, because, of course, we only have 12 months in the year.