The division method is a systematic way to find the prime factors of a given number. Here's how it works:
Steps for Finding Prime Factors Using the Division Method
The division method involves repeatedly dividing the number by the smallest possible prime number until you are left with 1.
Step 1: Divide by the Smallest Prime Number
- Start by dividing the given number by the smallest prime number, which is 2.
- Ensure that the prime number divides the number exactly (i.e., with no remainder). If 2 doesn't divide the number exactly, move on to the next prime number (3, 5, 7, 11, and so on).
Step 2: Divide the Quotient
- Take the quotient (the result of the division) from the previous step and again divide it by the smallest prime number that divides it exactly.
Step 3: Repeat Until the Quotient is 1
- Continue this process of dividing the quotient by the smallest possible prime number until you reach a quotient of 1.
- The prime factors are all the prime numbers you used as divisors during this process.
Example
Let's find the prime factors of 84 using the division method.
| Division | Quotient | Prime Factor |
|---|---|---|
| 84 ÷ 2 | 42 | 2 |
| 42 ÷ 2 | 21 | 2 |
| 21 ÷ 3 | 7 | 3 |
| 7 ÷ 7 | 1 | 7 |
Therefore, the prime factors of 84 are 2, 2, 3, and 7. We can express this as: 84 = 2 x 2 x 3 x 7.
