Question

The number 27 is special because it is three times the sum of its digits 27=3(2+7).

Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

Are there any three digit 'seven-up' numbers. Is it possible to find a number K such that there is a three digit number that is K times the sum of its digits (a K-up number)?

Answer 1

for your second question:

a = the tens digit (the first digit) of the 2-digit number
b= the ones digit (the second digit) of the 2-digit number.

therefore, the number is 10a + b

10a + b = 7(a + b)
3a=6b

this statement can only be logically equivalent if a = 6 and b = 3.

therefore. 63 = 7(6+3)

Answer 2

all seven-up numbers : according to @dgamma3 equation 3a=6b

a=2 ---> b=1 ----> 21
a=4 ---> b=2 ----> 42
a=6 ---> b=3 ----> 63
a=8 ---> b=4 ----> 84

Answer 3

sorry i gotta go ... @ganeshie8