When integer of 6 digits 5ABC15 becomes a multiple of 999, find the integer ABC of 3 digits.
Answer
Since it is 5ABC15/1000=5AB.C15, the quotient of 5ABC15 / 999 is also understood that it becomes three digits.
Assuming the three digits quotient is DEF and 999 = 1000 - 1, it is calculated as follows.
(1000 - 1) x DEF = DEF000 - DEF = 5ABC15
DEF000
- DEF
5ABC15
Based on this formula, it is found that D = 5, E = 8, F = 5.
Therefore, 585000 - 585 = 584415, then ABC = 844.
844
Solution
When 5ABC15 is divided by 999, it is considered what digit a quotient will be.
Since it is 5ABC15/1000=5AB.C15, the quotient of 5ABC15 / 999 is also understood that it becomes three digits.
Assuming the three digits quotient is DEF and 999 = 1000 - 1, it is calculated as follows.
(1000 - 1) x DEF = DEF000 - DEF = 5ABC15
DEF000
- DEF
5ABC15
Based on this formula, it is found that D = 5, E = 8, F = 5.
Therefore, 585000 - 585 = 584415, then ABC = 844.
