Understanding Numbers |
Integers are whole numbers (positive and negative, including zero). Thus this group may include numbers such as -2, -1, 0, 1, 2 and so forth. Natural numbers are positive integers. Square numbers are numbers that can be obtained by multiplying another number by itself. For example 36 is a square number because it is 6 x 6 and 25 is a square number because it is the product of 5 x 5. Prime numbers are numbers above 1 that cannot be divided by any number, other than 1 and itself to give an integer or whole number. This group includes numbers such as 2, 3, 5, 7, 11, 13, 17, 19. Some of these number types were covered in the posting Set Notation. You can refer to that posting for more information. Rational numbers are numbers that can be written as fractions, where numerator and denominator are integers. For example 1/2, 4, 1.75. Irrational numbers are numbers that cannot be written as fractions, such as pi. In decimal form these numbers go on forever and the same pattern of digits are not repeated. A factor of a number is a number which will divide into your number exactly, in other words without a remainder. So you can divide a number by one of its factors and you won't be left with a remainder. For example, 3 is a factor of 9 because you can divide 9 by 3 and you won't be left with a remainder. Decomposing numbers into factorsAny number can be written as the product of prime numbers in one way. For example, 30 = 5 x 6 . This number can be decomposed further into 5 x 3 x 2. Note that you can not further decompose these numbers. So, that right there is your solution. Why? because all the number in that list are prime numbers, thus there is nothing else that can you can divide them with other than 1 and themselves without getting a remainder. Example: Find the prime factor decomposition of 40. We look at 40 and try to find numbers which we can divide it by. We can see that it divides by 2. 2 is a prime number, but 20 is not. So we need to split 20 up into prime numbers. 20 = 5 × 4 , but 4 is still not a prime number because it can be divided by 2. Thus, 40 = 5 × 2 x 2 x 2 You can also take a look at Evaluating Algebraic expressions - Bodmas for more information. |
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