219968

219,968 is a positive integer. It is even and composite, with prime factorization 2^6 × 7 × 491, so 219,968 = 64 × 7 × 491 = 448 × 491. It has 28 positive divisors.

In arithmetic terms, the Euler totient of 219,968 is 94,080, computed as 219,968 × (1/2) × (6/7) × (490/491). The number is between the squares 469^2 = 219,961 and 470^2 = 220,900, and indeed 219,968 = 469^2 + 7, so it is not a perfect square.

Representations of 219,968 include binary, hexadecimal, and octal forms. In binary it is 110101101101000000₂. In hexadecimal it is 0x35B40. In octal it is 655500₈.

The factorization 2^6 × 7 × 491 indicates the number’s divisibility properties: it is divisible by 2, 4, 8, 16, 32, and 64, as well as by the odd factors 7 and 491, and by combinations thereof (for example 14, 28, 56, etc.). Its prime factors include two relatively small primes (2 and 7) and a larger prime (491). There is no widely noted special significance attached to 219,968 beyond its role as an example number in discussions of factorization and base conversions.

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