12345679

12345679 is an eight-digit integer obtained by removing the digit 8 from the nine-digit sequence 123456789. It is notable for a set of arithmetic properties that reveal patterns in base-10 multiplication and in decimal representations of fractions.

A key feature is its relationship to multiples of 9 and to repunits. For example, 12,345,679 × 9 equals 111,111,111, and 12,345,679 × 8 equals 98,765,432. Other straightforward multiplications also produce orderly results, such as 12,345,679 × 4 = 49,382,716; ×5 = 61,728,395; ×6 = 74,074,074; ×7 = 86,419,753; and ×9 = 111,111,111. Additionally, 12,345,679 × 81 equals 999,999,999, showing that the number is a divisor of 10^9 − 1.

In decimal expansions, 1/81 = 0.012345679012345679..., so the repeating block is 012345679, a sequence that contains every digit from 0 to 9 except 8. This connection highlights how 12345679 relates to repunits and to cyclic patterns in base-10 arithmetic.

Construction and patterns aside, 12345679 is frequently cited in recreational and educational contexts for illustrating how removing a digit from a consecutive sequence can yield a number with surprising multiplicative symmetry and connections to fundamental decimal representations.

See also: repunit, 111111111, 123456789.

---