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For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2. By the same principle, 10 is the least common multiple of −5 and −2 as well.
In arithmetic and algebra, the fifth power or sursolid [1] of a number n is the result of multiplying five instances of n together: n 5 = n × n × n × n × n. Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube. The sequence of fifth powers of integers is:
Powers of 2 appear in set theory, since a set with n members has a power set, the set of all of its subsets, which has 2 n members. Integer powers of 2 are important in computer science. The positive integer powers 2 n give the number of possible values for an n-bit integer binary number; for example, a byte may take 2 8 = 256 different values.
For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4 , or 20 / 5 = 4 . [ 2 ] In the example, 20 is the dividend, 5 is the divisor, and 4 is the quotient.
Two to the power of n, written as 2 n, is the number of values in which the bits in a binary word of length n can be set, where each bit is either of two values. A word, interpreted as representing an integer in a range starting at zero, referred to as an "unsigned integer", can represent values from 0 (000...000 2) to 2 n − 1 (111...111 2) inclusively.
If two divisions are done, a multiple of 5 · 5=25 rather than 5 must be used, because 25 can be divided by 5 twice. So the number of coconuts that could be in the pile is k · 25 – 4. k =1 yielding 21 is the smallest positive number that can be successively divided by 5 twice with remainder 1.
In mathematics, a multiple is the product of any quantity and an integer. [1] 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.
If 2 k + 1 is prime and k > 0, then k itself must be a power of 2, [1] so 2 k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023 [update] , the only known Fermat primes are F 0 = 3 , F 1 = 5 , F 2 = 17 , F 3 = 257 , and F 4 = 65537 (sequence A019434 in the OEIS ).