9×9×7×11

9×9×7×11 is a product of four integers whose value is 6237. The calculation can be grouped in different ways, for example 9×9=81 and 7×11=77, so 81×77=6237. Another valid grouping is (9×11)×(9×7) = 99×63 = 6237. The expression serves as a simple example of how multiplying several integers yields a single composite number.

Prime factorization and divisibility play a central role in understanding the number. The product 9×9×7×11 can be written as (3^2)×(3^2)×7×11, which equals 3^4 × 7 × 11. Consequently, 6237 is divisible by 3 and by 9 (since 3^4 appears in its factorization), and it is also divisible by 7 and 11. The factorization also shows that 6237 has multiple nontrivial divisors beyond 1 and itself.

Number of divisors and related sums can be derived from the prime factorization. For n = 3^4 × 7 × 11, the number of positive divisors is (4+1)×(1+1)×(1+1) = 5×2×2 = 20. The sum of all positive divisors is (3^5−1)/(3−1) × (7^2−1)/(7−1) × (11^2−1)/(11−1) = 121 × 8 × 12 = 11,616.

In summary, 9×9×7×11 equals 6237, a four-digit composite number with prime factorization 3^4 × 7 × 11, and it has 20 positive divisors with a total divisor sum of 11,616.