Has anyone asked you this before? Probably not (unless you‘ve seen me at the markets!). But it’s important - if your age is part of your identity, then surely so is the number of factors in your age!
Take a minute to work it out. (If you’ve forgotten what a factor is, it‘s a number that divides evenly into another number - your age in this case!).
Perhaps your age is a prime number? Primes have only 2 factors, 1 and the number itself, like 11 for example - it’s only factors are 1 and 11.
If you’re 12, however, you have 6 factors in your age, the most you’ve had in your life so far! They are 1, 2, 3, 4, 6, and 12 (because 12 = 1 x 12 = 2 x 6 = 3 x 4).
The table below shows the ages from 1 to 100, colour-coded by number of factors. Pink numbers only have 2 (prime numbers), light blue numbers have 4, and so on. Have a look at it. What do you see?
Ages 1-100 colour coded by number of factors
Wonder-provoking questions:
(Ideal for the classroom, or amongst your friends!)
1. Do you have more, less or the same number of factors compared to your previous birthday?
2. What is the chance of this happening? (assume you’ll live to 100!)
3. When was the last time you had this number of factors?
4. When is the next time that you will have the same number of factors in your age as you do now?
5. What’s the most factors you’ve had in your age so far?
6. At your next birthday, will you have more, less or the same number of factors?
7. Most number of factors
What’s the most number of factors you’re likely to have in your age?
What age does this happen?
How many years till you get there?
How many factors are in your answer to c?
8. Who has the most factors in their age in your family? Who has the least?
9. What’s the greatest factor difference that you’ve had in 2 consecutive years so far?
Isn’t this the reason for the Babylonians having had a base-60 numbering system, namely because it had so many factors? Perhaps you could elaborate on why that kind of numbering system worked for them. I’d also be interested to know why we have a base-10 system and what other cultures have used.