10002400

10002400, written in decimal as 10,002,400, is a natural number that follows 10,002,399 and precedes 10,002,401. It has mathematical significance mainly through its factorization and divisibility properties rather than any widely recognized name or special status.

The prime factorization of 10,002,400 is 2^5 × 5^2 × 12,503, where 12,503 is a prime number. This makes the number even and ensures it is divisible by 2, 4, 8, 16, and 32, as well as by 100 and by 400. It can be expressed as 800 × 12,503, and the total number of positive divisors is (5+1) × (2+1) × (1+1) = 36, reflecting its three distinct prime factors.

In decimal form, the digits sum to 1 + 0 + 0 + 0 + 2 + 4 + 0 + 0 = 7, so 10,002,400 is not a Harshad (Niven) number in base 10. Its last two digits are 00, confirming its status as a multiple of 100, and its factorization shows it is divisible by 400 as well (10,002,400 ÷ 400 = 25,006).

Overall, 10002400 is notable for its clean factorization into a small power of two, a square of five, and a relatively large prime, resulting in 36 divisors and straightforward divisibility properties.