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14 Divisors

What is the smallest number with exactly 14 divisors?

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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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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?

One to Eight

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?