Which number should fill the blank

Can you fill the blank with the correct number?

6 30 870 756030 _____




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The dirtier I get, the whiter I look. Who am I?

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A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

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Find the last number in the series below:

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Amazing Facts

Word ladder puzzle

The word ladder puzzle was invented by Lewis Carroll, author of Alice’s Adventures in Wonderland.