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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.
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 mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
Greatest common divisors can be computed by determining the prime factorizations of the two numbers and comparing factors. For example, to compute gcd(48, 180) , we find the prime factorizations 48 = 2 4 · 3 1 and 180 = 2 2 · 3 2 · 5 1 ; the GCD is then 2 min(4,2) · 3 min(1,2) · 5 min(0,1) = 2 2 · 3 1 · 5 0 = 12 The corresponding LCM is ...
A simple example is the Fermat factorization method, which considers the sequence of numbers :=, for := ⌈ ⌉ +. If one of the x i {\displaystyle x_{i}} equals a perfect square b 2 {\displaystyle b^{2}} , then N = a i 2 − b 2 = ( a i + b ) ( a i − b ) {\displaystyle N=a_{i}^{2}-b^{2}=(a_{i}+b)(a_{i}-b)} is a (potentially non-trivial ...
When one factor is an integer, the product is a multiple of the other or of the product of the others. Thus, is a multiple of , as is . A product of integers is a multiple of each factor; for example, 15 is the product of 3 and 5 and is both a multiple of 3 and a multiple of 5.