Welcome to our lesson on factors and multiples! These are fundamental concepts in arithmetic that describe relationships between numbers through multiplication and division. A factor is a number that divides another number exactly with no remainder, while a multiple is the result of multiplying a number by any whole number. Let's explore these concepts with visual examples.
Now let's learn how to find factors step by step using the number 12 as our example. First, we start with 1 and the number itself, which are always factors. Then we test each number between 1 and 12 to see if it divides 12 exactly with no remainder. Let's check: 12 divided by 1 equals 12, 12 divided by 2 equals 6, 12 divided by 3 equals 4, 12 divided by 4 equals 3, 12 divided by 6 equals 2, and 12 divided by 12 equals 1. All of these divisions give whole number results, so the factors of 12 are 1, 2, 3, 4, 6, and 12.
Now let's explore multiples using the number 5. Multiples are found by multiplying a number by whole numbers: 1, 2, 3, 4, 5, and so on. Let's calculate: 5 times 1 equals 5, 5 times 2 equals 10, 5 times 3 equals 15, 5 times 4 equals 20, 5 times 5 equals 25, and 5 times 6 equals 30. Notice the pattern: we keep adding 5 to get the next multiple. So the first six multiples of 5 are 5, 10, 15, 20, 25, and 30. This pattern continues infinitely.
Now let's understand the important relationship between factors and multiples. The key relationship is this: if A is a factor of B, then B is a multiple of A. For example, with the numbers 3 and 12: 3 is a factor of 12 because 3 divides 12 exactly, and 12 is a multiple of 3 because 12 equals 3 times 4. Here's a helpful memory tip: factors are usually smaller than or equal to the original number, while multiples are usually larger than or equal to the original number. This relationship helps us understand how multiplication and division connect these concepts.