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Originally, a product was and is still the result of the multiplication of two or more numbers.For example, 15 is the product of 3 and 5.The fundamental theorem of arithmetic states that every composite number is a product of prime numbers, that is unique up to the order of the factors.
For instance, 2 236 133 941 + 23# results in a prime, beginning a sequence of thirteen primes found by repeatedly adding 23#, and ending with 5 136 341 251. 23# is also the common difference in arithmetic progressions of fifteen and sixteen primes. Every highly composite number is a product of primorials (e.g. 360 = 2 × 6 × 30). [9]
An economical number has been defined as a frugal number, but also as a number that is either frugal or equidigital. gcd( m , n ) ( greatest common divisor of m and n ) is the product of all prime factors which are both in m and n (with the smallest multiplicity for m and n ).
For example, in the case of p = 10, a = 4, b = 15, composite number 10 divides ab = 4 × 15 = 60, but 10 divides neither 4 nor 15. This property is the key in the proof of the fundamental theorem of arithmetic. [note 2] It is used to define prime elements, a generalization of prime numbers to arbitrary commutative rings.
Here, 2 is being multiplied by 3 using scaling, giving 6 as a result. Animation for the multiplication 2 × 3 = 6 4 × 5 = 20. The large rectangle is made up of 20 squares, each 1 unit by 1 unit. Area of a cloth 4.5m × 2.5m = 11.25m 2; 4 1 / 2 × 2 1 / 2 = 11 1 / 4
6 is the 2nd superior highly composite number, [5] the 2nd colossally abundant number, [6] the 3rd triangular number, [7] the 4th highly composite number, [8] a pronic number, [9] a congruent number, [10] a harmonic divisor number, [11] and a semiprime. [12] 6 is also the first Granville number, or -perfect number. A Golomb ruler of length 6 is ...
The natural numbers 0 and 1 are trivial sum-product numbers for all , and all other sum-product numbers are nontrivial sum-product numbers. For example, the number 144 in base 10 is a sum-product number, because 1 + 4 + 4 = 9 {\displaystyle 1+4+4=9} , 1 × 4 × 4 = 16 {\displaystyle 1\times 4\times 4=16} , and 9 × 16 = 144 {\displaystyle 9 ...
In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal to 1. [2] [3] The integers k of this form are sometimes referred to as totatives of n. For example, the totatives of n = 9 are the six numbers 1, 2, 4, 5, 7 and 8.