Multiples, Factors and Prime Factors

Multiples: A multiple of a number is any number that can be evenly divided by that number. For example, multiples of 2 include 2, 4, 6, 8 and so on.
Finding Multiples: To find multiples of a number, simply multiply that number by 1, 2, 3, 4, 5 and so on. For instance, multiples of 5 are 5 (5 x 1), 10 (5 x 2), 15 (5 x 3), 20 (5 x 4) etc.
Common Multiples: A common multiple is a number that is a multiple of two or more numbers. For example, 12 is a common multiple of 3 and 4.
Factors: A factor is a number that divides into another number exactly, leaving no remainder. For example, the factors of 10 are 1, 2, 5 and 10, since these numbers divide evenly into 10.
Determining Factors: To determine the factors of a number, list all the numbers it can be divided evenly by. For instance, to find the factors of 12, divide 12 by all the numbers less than and equal to half of it. Here, the factors are 1, 2, 3, 4, 6, and 12.
Common Factors: A common factor is a number that will divide two or more other numbers exactly. For example, the common factors of 12 and 15 are 1 and 3.
Prime Factors: These are the factors of a number that are prime numbers. A prime number is a number that has only two distinct factors: 1 and itself.
Identifying Prime Factors: To identify prime factors of a number, begin division from the smallest prime number (which is 2) and go ahead with division till no more division is possible. For instance, the prime factors of 12 are 2 x 2 x 3.
Prime Factor Decomposition: This is the process of breaking down a number into its prime factors. This is done by progressively dividing the number by its smallest prime factor until all the factors are prime.
Highest Common Factor (HCF): The highest common factor of two or more numbers is the highest number that divides exactly into each of the numbers. It is found by comparing the prime factors of the numbers.
Lowest Common Multiple (LCM): The lowest common multiple of two or more numbers is the smallest number that is a multiple of each of the numbers. You can find it by listing the multiples of the numbers and finding the smallest one that appears in all the lists.

Remember, mastering the art of finding multiples, factors, and prime factors is a key step in advancing your knowledge in mathematics. Practice frequently with varying numbers to ensure understanding and precision.