212121

212,121, commonly written without comma as 212121, is the six-digit integer in base 10 formed by repeating the two-digit block 21 three times. It equals 21 × 10101 and can be factored as 3^2 × 7^2 × 13 × 37, yielding a prime factorization of 212,121 = 3^2 × 7^2 × 13 × 37.

The digit sum is 9, which confirms divisibility by 9; the number is odd, so not divisible by 2 or 5. The decimal representation is not a palindrome: reversing the digits gives 121212. The factorization shows it is divisible by 441 (which equals 21^2); 441 × 481 = 212,121, with 481 = 13 × 37.

In mathematical contexts, numbers with repeating blocks like 212121 often appear in discussions of multiples of repunits and in illustrating factorization patterns of products of small primes. Such numbers serve as concrete examples for teaching how decimal patterns relate to arithmetic structure.

Outside pure mathematics, 212121 can appear as a numeric string used in examples or as a model number or code, but this article concentrates on its numeric properties.