Is there an efficient way to work out how many factors a large number has?
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.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Alison and Charlie are playing a divisibility game with a set of $0-9$ digit cards.
They take it in turns to choose and place a card to the right of the cards that are already there.
And so on!
They keep taking it in turns until one of them gets stuck.
Click here to see an example of a game:
Play the game a few times on your own or with a friend.
Are there any good strategies to help you to win?
After a while, Charlie and Alison decide to work together to make the longest number that they possibly can that satisfies the rules of the game.
They very quickly come up with the five-digit number $12365$. Can they make their number any longer using the remaining digits? When will they get stuck?
What's the longest number you can make that satisfies the rules of the game?
Is it possible to use all ten digits to create a ten-digit number?
Is there more than one solution?
Please send us your explanation of the strategies you use to create long numbers.