3969

3969 is a natural number that is the square of 63, since 63 squared equals 3969. In base-10 notation it is written as 3969.

Mathematically, 3969 factors as 3^4 × 7^2, making it a perfect square. It can be expressed as 63^2 and also as 9 × 441. The digit sum is 3 + 9 + 6 + 9 = 27, so the number is divisible by 9; the digital root is 9. It is also a Harshad (Niven) number in base 10 because 3969 divided by 27 equals 147.

In Roman numerals, 3969 is written as MMMCMLXIX. This follows from 3000 (MMM) + 900 (CM) + 60 (LX) + 9 (IX).

In number theory, 3969 is notable as the square of 63, a product of 7 and 9. Its status as a four-digit perfect square and its factorization into small prime powers (3^4 × 7^2) are typical points of reference when illustrating square numbers and their properties. Beyond its mathematical characteristics, 3969 does not have widespread historical or cultural associations, but it serves as a representative example in discussions of squares, digit sums, and divisibility.