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A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N? ### Thirty Six Exactly

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors? ### Strange Numbers

All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either its first or its last digit. Find all strange numbers.

# One to Eight

##### Age 11 to 14 Challenge Level:

Here are some 'funny factorisations'. Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits $2$ to $9$ once and only once.

** $\times$ ** $= 4876$
** $\times$ ** $= 5394$

Now do the same with the digits $1$ to $8$ to complete the following expressions.

** $\times$ ** $= 1368$
$5$* $\times$ $6$* $=$ ****
$52$ $\times$ ** $=$ ****

Is there more than one solution?