# 105 (number)

105 (one hundred [and] five) is the natural number following 104 and preceding 106.

105
Cardinal one hundred [and] five
Ordinal 105th
(one hundred [and] fifth)
Numeral system 105
Factorization $3 \cdot 5 \cdot 7$
Divisors 1, 3, 5, 7, 15, 21, 35, 105
Roman numeral CV
Binary 11010012
Octal 1518
Duodecimal 8912

## In mathematics

105 is a triangular number, a 12-gonal number and a Zeisel number. It is a sphenic number, and is the product of three consecutive prime numbers. 105 is the double factorial of 7. It is also the sum of the first five square pyramidal numbers.

105 comes in the middle of the prime quadruplet (101, 103, 107, 109). The only other such odd numbers less than a thousand are 15, 195 and 825. 105 is also a pseudoprime to the prime bases 13, 29, 41, 43, 71, 83 and 97. The distinct prime factors of 105 add up to 15, and so do those of 104, hence the two numbers form a Ruth-Aaron pair under the first definition.

105 is also a number n for which n − 2k is prime, for 0 < k < log2(n). (This even works up to k = 8, ignoring the negative sign.)

105 is the smallest integer such that the factorization of xn − 1 over Q includes coefficients other than $\pm 1$.

105 is also:

## References

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