Math Problem : G.9 Product of two integers is 44448888

A is an integer of 4 figures and each digit is the same number.
As for B, each digit consists of two kinds of numbers for the integer of 4 figures.
The product of A and B is 44448888.
Find A and B.

Answer

A = 6666, B = 6668

Solution

According to the statement that A is an integer of 4 figures and each digit is the same number, A is a multiple of 1111, which is nine integers 1111 ~ 9999 are considered.
Moreover, 44448888 = 1111 × 40008 and since B is an integer of 4 figures, 40008 = (number of 1 figure of 1~9) × (integer of 4 figures).
40008 = 6 × 6668 = 8 × 5001.
Since B consists of two kinds of numbers, only 6 × 6668 is applied.
Therefore, A= 6666, B= 6668.