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Terms in this set (11)
Integer
An integer is any positive or negative whole number or zero. The ASVAB often requires you to work with integers, such as -6, 0, or 27
Numerical factors
factors are integers (whole numbers) that can be divided evenly into another integer. To factor a number, you simply determine the numbers that you can divide into it. For example, 8 can be divided by the numbers 2 and 4 (in addition to 1 and 8), so 2 and 4 are factors of 8. The prime factorization of the number 30 is written 2 x 3 x 5.
Numbers may be either composite or prime, depending on how many factors they have.
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Composite number
A composite number is a whole number that can be divided evenly by itself and by 1, as well as by one or more other whole numbers; in other words, it has more than two factors. Examples of composite numbers are 6 (whose factors are 1, 2, 3, and 6), 9 (whose factors are 1, 3, and 9), and 12 (whose factors are 1, 2, 3, 4, 6, and 12).
Composite number list
4 = 2 x 2 =
6 = 2 x 3 =
8 = 2 × 2 × 2 =
9 = 3 × 3 =
10 = 2 × 5 =
12 = 2 × 2 × 3 =
14 = 2 × 7 =
15 = 3 × 5 =
16 = 2 × 2 × 2 × 2 =
18 = 2 × 3 × 3 =
20 = 2 × 2 × 5 =
21 = 3 × 7 =
22 = 2 × 11 =
24 = 2 × 2 × 2 × 3 =
25 = 5 × 5 =
26 = 2 × 13 =
27 = 3 × 3 × 3 =
28 = 2 × 2 × 7 =
30 = 2 × 3 × 5 =
32 = 2 × 2 × 2 × 2 × 2 =
33 = 3 × 11 =
34 = 2 × 17 =
35 = 5 × 7 =
36 = 2 × 2 × 3 × 3 =
38 = 2 × 19 =
39 = 3 × 13 =
40 = 2 × 2 × 2 × 5 =
42 = 2 × 3 × 7 =
44 = 4 × 11 =
45 = 3 × 3 × 5 =
46 = 2 × 23 =
48 = 2 × 2 × 2 × 2 × 3 =
49 = 7 × 7 =
50 = 2 × 5 × 5 =
Prime factorization
Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers. Here, all the concepts of prime factors and prime factorization methods have been explained which will help the students understand how to find the prime factors of a number easily.
The simplest algorithm to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, prime factorising the number 30 we get, 30/2 = 15, 15/3 = 5, 5/5 = 1. Since we received the remainder, it cannot be further factorised. Therefore, 30 = 2 x 3 x 5, where 2,3 and 5 are prime factors.
The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19 and so on. These prime numbers when multiplied with any natural numbers produce composite numbers. In this article, let us discuss the definition of prime factorization, different methods to find the prime factors of a number with solved examples.
Prime number
A prime number is a whole number that can be divided evenly by itself and by 1 but not by any other number, which means that it has exactly two factors. The number 1 is not a prime number. Examples of prime numbers are 2 (whose factors are 1 and 2), 6 (whose factors are 1 and 5), and 5 (whose factors are 1 and 5), and 11 (whose factors are 1 and 11).
Prime number list
2 =
3 =
5 =
7 =
11 =
13 =
17 =
19 =
23 =
29 =
31 =
37 =
41 =
43 =
47 =
Base
A base is a number that's used as a factor a specific number of times - it's a number raised to an exponent. For instance, the term 4^3 ( which can be written 4 x 4 x 4, and in which 4 is a factor three times) has a base of 4.
Exponent
an exponent is a shorthand method of indicating repeated multiplication. For example, 15 x 15 can also be expressed as 15^2, which is also known as "15 squared" or "15 to the exponent, and it indicates the number of times you multiply the base by itself. Note that 15^2 (15 x 15) which equals 225, isn't the same as 15 x 2 (which equals 30).
To express 15 x 15 x 15 using this shorthand method, simply write it as 15^3, which is also called "15 cubed" or "15 to the third power." Again, 15^3 (which equals 3,375) isn't the same as 15x3 (which equals 45).
Square root
The square root of a number is the number that, when multiplied by itself (in other words, squared), equals the original number. For example, the square root of 36 is 6. If you square 6, or multiply it by itself, you produce 36. (Check out "Getting to the Root of the Problem" later in this chapter.
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