Base 13?

Number Theory Level 3

What single digit number would need to be subtracted from the following base 13 number to make it divisible by 13?

98743298742734987547657644211154547

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The answer is 7.

1 solution

Geoff Pilling
Apr 14, 2016

Any base $n$ number will be divisible by $n$ if, and only if, the number ends in 0. So subtracting 7 will do the job! :)

can you please elaborate?

unable to understand

thanks!!! :-)

Atul Shivam - 5 years, 2 months ago

Sure thing... In base 13, reading the digits from right to left, this number is equal to $7*13^0 + 4*13^1 + 5*13^2 + 4*13^3 + ...$ . And all except for the first element, $7x13^0$ , divide by 13. Therefore, if we subtract 7, that element goes away and then the number is divisible by 13.

It's similar to how any number in decimal that ends with a zero divides by 10.

Geoff Pilling - 5 years, 2 months ago

Base 13?

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The answer is 7.

1 solution

unable to understand

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