The word integer is another word for a whole number, such as 23, 560 or 190,000,000. Integers can be positive (such as 455 or 3) or negative (such as -78 or -1,663). The number zero, 0, is also an integer.
Numbers which are decimal numbers, such as 0.042 and 5,799.2, are called real numbers or floating point numbers. They can also be positive or negative, and you can easily spot them as they contain a decimal point.
If one number integer can be divided by another integer an exact number of times then the first number is said to be a multiple of the second, and the second number is said to be a factor of the first.
For example, 48 is a multiple of 6 because 6 goes into 48 an exact number of times (8 times in this case). Similarly, 6 is a factor of 48.
On the other hand, 48 is not a multiple of 5, because 5 doesn't go into 48 an exact number of times. 5 is not a factor of 48.
When two numbers (integers or real numbers) are added together, the result is called the sum. For instance, the sum of 3 and 6 is 9, and the sum of 70 and 24.07 is 94.07.
When one number is subtracted from another, the result is called the difference. For instance the difference between 12 and 8 is 4, as 12 - 8 = 4.
When one number is multiplied by another, the result is called the product. For example, the product of 5.1 and 11.4 is 58.14, as 5.1 x 11.4 = 58.14.
When one number is divided by another, the result of the division is called the quotient. If the original numbers were integers, then there may be a remainder, depending on how the division is done. Some people prefer to give the result in terms of a quotient and a remainder, some prefer to give it as a decimal answer. For example, suppose you had the following calculation:
72 ¸ 8 (where ¸ means "divided by")
In this case, the quotient is 9 (i.e. the answer to the division is 9) and there is no remainder. With the following calculation:
128 ÷ 10
you have a choice. You can either say that the quotient is 12 and the remainder is 8 (i.e. 10 goes 12 times into 128 with 8 left over), or you can say that the answer is 12.8, in which case there is no remainder. The choice is yours.
Integers such as 5, 6, 7, 8, 9 are called consecutive integers, because they follow on from each other. Integers such as 46, 48 50, 52 are called consecutive even integers. Integers such as 103, 105, 107, 109 are called consecutive odd integers.
You can go even further than that if you like: 4, 8, 12 and 16 are consecutive multiples of 4, as they are all multiples of 4 and there are no other multiples of 4 between 4 and 16. However, although 7, 14, 28 and 35 are all multiples of 7, they are not consecutive multiples of 7 as I have forgotten to mention that 21 is also a multiple of 7 and should sit in the middle of that list (you probability noticed that it wasn't there!)
Odd and Even Numbers
Any number which is a multiple of 2 is called an even number. For instance, 4, -50, 7346 and -100 are all even numbers. In general, if x is any integer (even or not), then 2x will be an even integer, because it is a multiple of 2. Also x raised to any positive integer power will be an even number, so x2, x3, x4 etc. will be even numbers.
Any whole number which is not a multiple of 2 is called an odd number. For instance, -1, 3, 6883 and -8147 are all odd numbers. Any odd number raised to an positive integer power will also be an odd number, so if x is an odd number, then so will x2, x3, x4 etc. be odd numbers.
