Question

What natural number is 5 times the sum of its digits? What natural number is 5 times the sum of its digits? @Mathematics

Answer 1

45.

4+5 = 9
9*5 = 45

Answer 2

ok

Answer 3

thanks

Answer 4

now try proving why 45 is the only one...

Answer 5

k can you ansewr my question please its at the top

Answer 6

I get why its 45

Answer 7

if the answer was a single digit number d1, then:\[d_1=5d_1\]which is only true if the digit is zero. So zero could be one solution.
if the answer is a 2 digit number d1d2, then:\[10d_1+d_2=5(d_1+d_2)=5d_1+5d_2\]\[5d_1=4d_2\]this is satisfied if d1=4, d2=5, so 45 is another solution.
if answer is a 3 digit number d1d2d3, then:\[100d_1+10d_2+d_3=5(d_1+d_2+d_3)=5d_1+5d_2+5d_3\]\[95d_1+5d_2=4d_3\]the maximum that d3 can be is a 9, and 4*9 is 36 which can never equal 95*anything, so 3 or more digits is impossible.
so only solutions are: 0, 45

Answer 8

I guess (for the number of solutions) it all depends on whether or not one includes 0 as a natural number.

Answer 9

k can you answer my other ques.