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14 Divisors

What is the smallest number with exactly 14 divisors?

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Repeaters

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.

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Oh! Hidden Inside?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Differences

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

Choose any three whole numbers, find the differences between them all, and find the product of the differences.

For example, if your three whole numbers are $7$, $4$ and $12$, the differences are:

$12 - 7 = 5$
$12 - 4 = 8$
$7 - 4 = 3$

The product of the differences is $3\times 5\times 8 = 120$

Try a few examples.

What do you notice?
Can you explain what you've noticed?

 

Now choose any four whole numbers, find the differences between them all, and find the product of the differences.

For example, if your four whole numbers are $7$, $4$, $12$ and $6$, the differences are:

$7-4 = 3$
$12-7 = 5$
$7-6 = 1$
$12-4 = 8$
$6-4 = 2$
$12-6 = 6$

The product of the differences is $3\times 5\times 1\times 8\times 2\times 6 = 1440$

Try a few examples.

What do you notice?
Can you explain what you've noticed?