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Factors are the building blocks of numbers. To understand factors, consider them as the numbers you can multiply together to get another number. Let's take 12 as an example. The factors of 12 are all the whole numbers that can be multiplied in pairs to make 12. This includes:

• 1 and 12, because 1 times 12 equals 12
• 2 and 6, since 2 times 6 equals 12
• 3 and 4, as 3 times 4 equals 12

Notice that each of these factor pairs multiplies to give a product of 12. A factor is essentially any number that can be divided exactly into another number, without leaving a remainder. In the case of 12, we listed the factors: 1, 2, 3, 4, 6, and 12. Understanding factors is vital because they help us determine the greatest common factor (GCF) of two numbers.

Multiples are what you get when you multiply a number by an integer. Let's stick with 12 for an example. The multiples of 12 are all the numbers you get by multiplying 12 by any whole number, like:

• 12 x 1 = 12
• 12 x 2 = 24
• 12 x 3 = 36
• And so on…

Multiples of a number extend into infinity because you can keep multiplying by higher integers. They’re crucial in identifying numbers that share a common factor, like when you look for numbers whose GCF is a particular value. In the exercise above, we chose 24 and 36 as two numbers with a GCF of 12 because both are multiples of 12.

Divisibility refers to a number's ability to be divided by another number without leaving a remainder. A number is divisible by its factors. For any two numbers, identifying common divisors helps find the greatest common factor (GCF). For instance, if you check if 24 and 36 are divisible by 12, both divide perfectly:

• 24 divided by 12 equals 2
• 36 divided by 12 equals 3

Each leaves no remainder, confirming they're divisible by 12. Checking divisibility is particularly useful when you need to verify the GCF of two numbers. By listing their divisors or factors, you can compare and find the highest number that divides both completely. In cases like 24 and 36, you can confidently state their GCF is 12 due to their divisibility by that number.