Factors and multiples are two key concepts in mathematics that are always studied together as they both involves multiplication. Let us learn about multiples and factors and how they relate to each other.
When two or more numbers are multiplied, the product is called the multiple of each of the numbers being multiplied. Let us understand this with an example:
3 × 5 = 15
Here 15 is the multiple of 3 and 5.
To find the multiples of a number, multiply it by 1, 2, 3, 4 and so on
First 11 multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33
First 11 multiple of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
A number that is a multiple of two or more numbers is called a common multiple. For example, let's find the two common multiples of 3 and 4 are.
Multiples of 3 are 3,6,9,12,15,18, 21, 24, 27, 30, ...
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
First two common multiples of 3 and 4 are 12, 24
When two or more numbers are multiplied the answer is called the product and each of the numbers being multiplied is called the factor of the product.
Let us understand this using an example. Find the factors of 12.
Now the factors of 12 are the numbers that produce the result as 12 when two numbers are multiplied together. Start with 1.
1 × 12 = 12
2 × 6 = 12
3 × 4 = 12
4 × 3 = 12 (so we have reached to a point where the numbers are repeating again)
Factors of 12 are 1, 2, 3, 12, 6 and 4
When we find the factors of two or more numbers, and then find some factors that are common or the same, then they are the common factors. For example, find the common factors of 18 and 27.
Factors of 18 are:
1 × 18, 2 × 9, 3 × 6
Factors of 27 are
1 × 27, 3 × 9
Factors of 18 are 1, 2, 3, 6, 9, 18
Factors of 27 are 1, 3, 9, 27
Therefore, common factors are 1, 3, and 9.
