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Number Theory Level 1

Is 986244 divisible by 13?

Yes No Insufficient information This question is flawed

2 solutions

Michael Fuller
Jan 12, 2016

From Divisibility Rules , we see that a positive integer $N$ is divisible by $13$ if and only if $4$ times the last digit of $N$ plus the number obtained by removing the units digit of $N$ is a multiple of $13$ also. Applying the rule, we get:

$\large 986244 ~\Rightarrow~ 98624 + 4 \times 4 = 98640 ~\Rightarrow ~9864 + 4 \times 0 = 9864$

$\large ~\Rightarrow ~986 + 4 \times 4 = 1002 ~\Rightarrow ~100 + 4 \times 2 = 108 ~\Rightarrow~ 10 + 4 \times 8 = 42$

From here we see that $42$ is not divisible by $13$ , and therefore $986244$ is also not divisible by $13$ .

Combined test for divisibility for 7, 11 and 13

Step 1 : make groups of 3 digits from the end in above case 986 244

Step 2 : Add groups at odd places and at even places. in above case group at odd place is only one, i.e. 244 and group at odd place is also only one i.e. 986

Step 3 : Find the difference in additions in above case it is 986 – 244 = 742

Step 4 : if the difference obtained is divisible by 7, 11 and 13 then the given number is divisible by 7, 11, 13

In above case 742 is divisible by 7, not divisible by 13 and not divisible by 11

So number 986244 is divisible by 7 and not divisible by 11 and 13

Sunil Pradhan - 4 years ago

Ariijit Dey
Nov 29, 2017

yOU CAN WRITE A PYTHON CODE IFF YOU DON'T WANNA USE A CALCULATOR

:-p :-p

How do u do dat?

Samson Ilerioluwa Adedokun - 3 years, 5 months ago

Search for the Pelimdrome code and you’ll find the answer :)

A Former Brilliant Member - 2 years, 3 months ago

Don't Use A Calculator!

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