Multiples and factors are mathematical terms used to describe the relationships between numbers.
Factors: A factor is a number that divides into another number exactly without leaving any remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Multiples: A multiple is a number that is obtained by multiplying a given number by any integer. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
It is important to note that every number has at least two factors, 1 and itself, while every number has an infinite number of multiples.
Multiples and factors are related in the sense that if a number is a multiple of another number, then the second number is a factor of the first number. For example, 12 is a multiple of 6, so 6 is a factor of 12.
Similarly, if a number is a factor of another number, then the second number is a multiple of the first number. For example, 4 is a factor of 12, so 12 is a multiple of 4.
Knowing the factors and multiples of a number is important in many areas of mathematics, including prime factorization, finding common denominators, and simplifying fractions.
Example 1:
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, ...
Example 2:
- Factors of 15: 1, 3, 5, 15
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Example 3:
- Factors of 11: 1, 11
- Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
Example 4:
- Factors of 8: 1, 2, 4, 8
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
In each example, you can see that the factors are the numbers that divide evenly into the given number, while the multiples are the numbers that result from multiplying the given number by another integer.