Divisibility Test II

Number Theory Level 1

Take any positive two digit number. Reverse its digits to obtain a new number. Out of the two numbers, subtract the smaller number from the larger number. The number which you get after subtraction will always be divisible by

9 2 10 11

Shabarish Ch by Shabarish Ch , 22, India

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2 solutions

Pethree Asiain
Mar 30, 2014

We just basically follow what the problem states, write it down and simplify it to find our answer. The difference of the two numbers = 10a+b-a-10b = 9a-9b = 9(a-b) This new number has a factor of 9 therefor it will always be divisible by 9. whether it is positive or negative. For example: 47-74=27 which as we can see is divisible by 9

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Rishikant Pandey
Mar 4, 2014

write no as 10a+b and do as the ques says.

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it is not true to all 2 digit positive integers, 11, 22, 33, ...

Kenneth Hermosisima - 7 years, 2 months ago

if you take 13 as the example then it wont work

Deepanshu Dochaniya - 7 years, 3 months ago

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13's digits reversed are 31,

31-13=18

which is divisible by 9

Yan Yau Cheng - 7 years, 3 months ago

13's digits reversed are 31, 31-13=18 which is divisible by 9

Prajwal Kavad - 7 years ago

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