- Prime Numbers Factors and Multiples
- Home
- Even and Odd Numbers
- Divisibility Rules for 2, 5, and 10
- Divisibility Rules for 3 and 9
- Factors
- Prime Numbers
- Prime Factorization
- Greatest Common Factor of 2 Numbers
- Greatest Common Factor of 3 Numbers
- Introduction to Distributive Property
- Understanding the Distributive Property
- Introduction to Factoring With Numbers
- Factoring a Sum or Difference of Whole Numbers
- Least Common Multiple of 2 Numbers
- Least Common Multiple of 3 Numbers
- Word Problem Involving the Least Common Multiple of 2 Numbers

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Factors

**Factors** are the numbers we multiply to get another number. For example, if we multiply 3 and 5, we get 15. We say, 3 and 5 are factors of 15.

Alternatively, factors of a number are those numbers which divide that number without leaving any remainder.

For **example**, 1, 2, 3, 4, 6, and 12 are factors of 12 as all of them divide it evenly.

### The largest and smallest factors of a number

- The largest factor of any number is the number itself and the smallest factor is 1.
- 1 is the factor of every number.
- So, for example, the largest and smallest factors of 12 are 12 and 1.

Find all the factors of 20

### Solution

**Step 1:**

We go through the whole numbers as shown below in table.

To find factors, we try to make products equal to 20.

**Step 2:**

We stop when get to a factor that repeats.

**Step 3:**

So all factors of 20 are 1, 2, 4, 5, 10, and 20

Find all the factors of 36

### Solution

**Step 1:**

We go through the whole numbers as shown.

To find all factors, we try to make products equal to 36.

**Step 2:**

We stop when get to a factor that repeats.

**Step 3:**

So all the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36