Mastering the Art of Factoring: A Comprehensive Guide to Breaking Down Numbers into Prime Factors

Factoring numbers

Factoring is the process of breaking down a number into its prime factors

Factoring is the process of breaking down a number into its prime factors. In other words, it involves finding all the numbers that can be multiplied together to give the original number.

To factor a number, you can follow these steps:

Step 1: Start by dividing the number by the smallest prime number, which is 2. Repeat this process until the number is no longer divisible by 2. Keep track of how many times you can divide the number by 2.

Step 2: Move on to the next prime number, which is 3. Divide the number by 3, again repeating this process until the number is no longer divisible by 3. Keep track of how many times you can divide the number by 3.

Step 3: Continue this process with all subsequent prime numbers (5, 7, 11, 13, etc.) until the number cannot be divided any further.

Step 4: The factors of the original number are obtained by multiplying the prime numbers together the same number of times that you divided the original number by each prime number.

Let’s use an example to understand this process. Suppose we want to factor the number 72.

Step 1: Divide 72 by 2 repeatedly until it is no longer divisible by 2:
72 ÷ 2 = 36
36 ÷ 2 = 18

Step 2: Divide 18 by 3 repeatedly until it is no longer divisible by 3:
18 ÷ 3 = 6

Step 3: Since the number 6 is no longer divisible by any prime number higher than 3, we have completed the factoring process.

Step 4: Now, multiply the prime numbers (2 and 3) together the same number of times that we divided the original number by each prime number:
2 × 2 × 2 × 3 = 24

Therefore, the prime factors of 72 are 2, 2, 2, and 3, and when multiplied together, they give the original number 72.

In summary, factoring numbers involves dividing the number by prime numbers until it cannot be divided any further, and then multiplying the prime factors together to obtain the original number. This process is useful in various mathematical applications, such as simplifying fractions, solving equations, and finding common factors.

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