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It is the third (or second) dodecahedral number, [4] and the sum of the first seven triangular numbers (1, 3, 6, 10, 15, 21, 28), which makes it the seventh tetrahedral number. [5] The number of divisors of 84 is 12. [6] As no smaller number has more than 12 divisors, 84 is a largely composite number. [7]
lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n). gcd( m , n ) × lcm( m , n ) = m × n . Finding the prime factors is often harder than computing gcd and lcm using other algorithms which do not require known prime factorization.
231 is also a multiple of 3: one has 231 = 3 · 77, and thus n = 2 · 3 2 · 77. Continue with 77, and 3 as a first divisor candidate. 77 is not a multiple of 3, since the sum of its digits is 14, not a multiple of 3. It is also not a multiple of 5 because its last digit is 7. The next odd divisor to be tested is 7.
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
If a factor already has natural units, then those are used. For example, a shrimp aquaculture experiment [9] might have factors temperature at 25 °C and 35 °C, density at 80 or 160 shrimp/40 liters, and salinity at 10%, 25% and 40%. In many cases, though, the factor levels are simply categories, and the coding of levels is somewhat arbitrary.
Integer factorization is the process of determining which prime numbers divide a given positive integer.Doing this quickly has applications in cryptography.The difficulty depends on both the size and form of the number and its prime factors; it is currently very difficult to factorize large semiprimes (and, indeed, most numbers that have no small factors).
In other words, for the quantities a and b, it can be said that b is a multiple of a if b = na for some integer n, which is called the multiplier. If a is not zero, this is equivalent to saying that / is an integer. When a and b are both integers, and b is a multiple of a, then a is called a divisor of b. One says also that a divides b.
The prefixes from tera-to quetta-are based on the Ancient Greek or Ancient Latin numbers from 4 to 10, referring to the 4th through 10th powers of 10 3. The initial letter h has been removed from some of these stems and the initial letters z , y , r , and q have been added, ascending in reverse alphabetical order, to avoid confusion with other ...