7638

7638 is a natural number that follows 7637 and precedes 7639. In base-10 notation, it is an even and composite integer.

Mathematical properties and factors

The prime factorization of 7638 is 2 × 3 × 19 × 67. Consequently, it has 16 positive divisors: 1, 2, 3, 6, 19, 38, 57, 114, 67, 134, 201, 402, 1273, 2546, 3819, and 7638. The number is divisible by 2, 3, and 6 (since 7638 ÷ 6 = 1273). Its digit sum is 7 + 6 + 3 + 8 = 24, so it is divisible by 3 but not by 9. Euler’s totient function for 7638 is φ(7638) = 2376.

Representations in other bases

In hexadecimal, 7638 equals 0x1DD6. In binary, it is 1110111010110. In octal, the representation is 16726. These representations reflect the same value expressed in different positional numeral systems.

Notes

As a product of four distinct primes, 7638 is squarefree. It does not form a perfect power and does not belong to common small-integer sequences beyond its basic arithmetic properties. In mathematical contexts, it serves as an example of a modest, highly composite-type structure arising from the product of small primes.