 The factors of a positive Whole number are those numbers which will divide evenly into it, without a remainder. For example, the factors of 6 are 1, 2, 3, and 6. Similarly the factors of 9 are 1, 3, and 9. Every number will have at least two factors, 1 and the number itself. Numbers whose only factors are 1 and the number itself are called PRIME. As an example, 17 is prime because its only factors are 1 and 17. Find out more about prime numbers here. Numbers which have more than those two factors are called COMPOSITE. For example, 12 is composite because its factors are 1 and 12, as well as 2, 3, 4, and 6. In order to find the factors of a number quickly, you need to have the times tables memorized. You may also have to use a calculator. For example, is 18 a factor of 72? You may need a calculator to check that 72 ÷ 18 = 4, so the answer is yes. However, if you have the times tables memorized you will save a lot of time, not needing to use a calculator to know that, for example, 108 divides by 9, or 132 divides by 11. When finding a number's factors it is helpful to write them in pairs. For example, if 48 divides evenly by 6, when you divide you will get another factor, in this case 8. Here are all the factors of 36: 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6. Here are all the factors of 20: 1, 20 2, 10, 4, 5 The GREATEST COMMON FACTOR for two or more numbers is the largest factor that is common to all the numbers. For example, consider the numbers 24 and 36: The factors of 24 are 1, 24, 2, 12, 3, 8, 4, 6 In order: 1, 2, 3, 4, 6, 8, 12, 24 The factors of 36 are 1, 36, 2, 18, 3, 12, 4, 9, 6 In order: 1, 2, 3, 4, 6, 9, 12, 18, 36 The greatest common factor (GCF) for 24 and 36 is 12. Here's another example: Find the greatest common factor for 60 and 96: Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 The GCF for 60 and 96 is 12. You can also find the GCF for three numbers: Find the GCF for 18, 45 and 81: 18: 1, 2, 3, 6, 9, 18 45: 1, 3, 5, 9, 15, 45 81: 1, 3, 27, 9, 81 GCF = 9 Sometimes the greatest common factor is just 1: Find the GCF for 18 and 25: 18: factors are 1, 2, 3, 6, 9, 18 25: factors are 1, 5, 25 GCF = 1 When this happens, the numbers 18 and 25 are said to be mutually prime. There is a quicker way to find the greatest common factor, but you'll need to review finding a number's prime factors first. Let's look at this example: Find the GCF for 18, 24 and 30: Let's find the prime factors of each number: 18: 2x3x3 24: 2x2x2x3 30: 2x3x5 The GCF is built from the least number of each prime factor: We need one 2 and one 3 (no 5's, because there are none in the first two numbers) GCF = 2x3 = 6 This is quicker if you know the times tables because prime factors are often small and you won't need a calculator to find them. Here's another example: Find the GCF for 8, 20, 36 and 50: Find the prime factors of each number: 8: 2x2x2 20: 2x2x5 36: 2x2x3x3 50: 2x5x5 We need one 2, but no 3's or 5's because there are none in 8 GCF = 2 Another example: Find the GCF for 16, 21 and 30: Find the prime factors of each number: 16: 2x2x2x2 21: 3x7 30: 2x3x5 We need no 2's (21 has none), no 3's (16 has none), no 5's (16 has none) and no 7's (16 has none) The GCF must be just 1. |