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Counting Factors

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.

Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

Statement Snap

Age 7 to 14 Challenge Level:

You might like to take a look at the problem Satisfying Statements, as the game and the problem complement one another.

You'll need to know your number properties to win a game of Statement Snap... 

To play the game, you'll need to print and cut out this set of cards
This game works well for 2 to 4 players.

How to play
Shuffle the cards, and place them face down on the table.
Turn over two cards so that all the players can see them.
The object of the game is to find a number that satisfies the statements on both cards.

For example, if the cards said "A multiple of 6" and "A factor of 90" you could pick the number 30.

After ten seconds, everyone declares a number that satisfies both cards, and then the next round begins by turning over the next two cards.

There are a few different scoring options for the game:
  • Score a point if you find a number that satisfies both cards
  • Score a point if you think of the highest number that satisfies both cards
  • List as many numbers as you can that satisfy both cards, and then score a point for each one.
  • List as many numbers as you can, and then score a point for each number on your list that doesn't appear on anybody else's list.

Impossible pairs!
Sometimes there might not be any numbers that satisfy both statements! If this happens, you can replace one of the cards with a new one.

A Final Challenge
Once you have played the game a few times, click below to see a few questions to explore:

How many impossible pairs can you find?
Can you find a number that satisfies 3 cards? Or 4 cards? Or...?