Six-Digit Multiplier

A six-digit number. One multiplier. One very surprising result.

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NEED A HINT?

HINT 1

Start with F. Since ABCDEF × F = 999,999, F must be a one-digit divisor of 999,999.

HINT 2

Test those possible values of F. Remember that 999,999 ÷ F must give a six-digit number ending in F, with six different digits.

ANSWER

A=1, B=4, C=2, D=8, E=5, F=7, with the check 142857 × 7 = 999,999.

Since F is the final digit as well as the multiplier, test the one-digit divisors of 999,999. Only F = 7 gives a six-digit quotient ending in 7 with six different digits: 999,999 ÷ 7 = 142857.