Answer: (originally answered by DeanR so credit to him)
x=6
Step-by-step explanation:
x3579x = 100000 x + 35790 + x
100000 = 2380 × 42 + 40
35790 = 852×42 + 6
Working mod 42,
100000 x + 35790 + x = 40 x + 6 + x = 41x + 6 = 6-x (mod 42)
So basically we need 6-x to be a multiple of 42, so between 0 and 9 that's x=6.
So our number is
635796 = 15138 × 42
