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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.
Here, 3 (the multiplier) and 4 (the multiplicand) are the factors, and 12 is the product. One of the main properties of multiplication is the commutative property, which states in this case that adding 3 copies of 4 gives the same result as adding 4 copies of 3: = + + + =
This representation is commonly extended to all positive integers, including 1, by the convention that the empty product is equal to 1 (the empty product corresponds to k = 0). This representation is called the canonical representation [10] of n, or the standard form [11] [12] of n. For example, 999 = 3 3 ×37, 1000 = 2 3 ×5 3, 1001 = 7×11×13.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. ... 3, 4, 6, 9, 13, 19, ... The number of cows each year if ...
A census taker approaches a woman leaning on her gate, number 14, and asks about her children. She says, "I have three children and the product of their ages is seventy–two. The sum of their ages is the number on this gate." The census taker does some calculation and claims not to have enough information.
This is because there are integers that 7 may be multiplied by to reach the values of 14, 49, 0 and −21, while there are no such integers for 3 and −6. Each of the products listed below, and in particular, the products for 3 and −6, is the only way that the relevant number can be written as a product of 7 and another real number:
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A sphenic number has Ω(n) = 3 and is square-free (so it is the product of 3 distinct primes). The first: 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154 (sequence A007304 in the OEIS ). a 0 ( n ) is the sum of primes dividing n , counted with multiplicity.