divisible?

Number Theory Level pending

what is divisible by 3? 12345678, 12345676, 11111111 or 12311111

3 4 2 1 all are divisible by 3

2 solutions

Emma P
Oct 6, 2018

My way is to keep adding all the numbers together until you get a 0123456789 number, and if it ends up as 3,6 or 9 then it is divisible by 3.

1+2+3+4+5+6+7+8= 36, 3+6=9

1+2+3+4+5+6+7+6= 34, 3+4=7

1+1+1+1+1+1+1+1= 8

1+2+3+1+1+1+1+1=11, 1+1=2

So only 12345678 ended up as 3, 6 or 9

X X
Sep 22, 2018

The digit sum of 12345678 is 36, which is divisible by 3.

The digit sum of 12345676 is 34, which isn't divisible by 3.

The digit sum of 11111111 is 8, which isn't divisible by 3.

The digit sum of 12311111 is 11, which isn't divisible by 3.

Hence the answer is 12345678, which is the first one.

Check my trick in finding numbers divisible by 3. That will really help in case of very big numbers such as : $12345985674291648693262354897326$ Now by doing with my method we will get : ${\color{#3D99F6}45 \quad 63 \quad 72 \quad 18 \quad 9 \quad 54 \quad216 \quad 9 \quad 63 \quad 63 \quad 9 \quad 54 \quad 72 \quad 36 \quad 9} \quad {\color{#20A900}484} = 16$ Hence the number is not divisible by 3 as 16 is not divisible by 3.

Ram Mohith - 2 years, 8 months ago

You can exclude all 3s, and it will become

12 3 45 9 567 42 9 81 6 48 693 63 225 48 9 732 6 (and it is divisible by 3)

X X - 2 years, 8 months ago

your way is very good but my way is say getting 123456789 and adding all the numbers together and getting ether 3,6 or 9. In this case 1+2+3+4+5+6+7+8+9= 45 then add the 4 and the 5 and get 9, so you CAN divide 123456789 into 3

Emma P - 2 years, 8 months ago

Yes. It is also good.

Ram Mohith - 2 years, 8 months ago

divisible?

2 solutions

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