Q: What is the prime factorization of the number 74,925?

 A:
  • The prime factors are: 3 x 3 x 3 x 3 x 5 x 5 x 37
    • or also written as { 3, 3, 3, 3, 5, 5, 37 }
  • Written in exponential form: 34 x 52 x 371

Why is the prime factorization of 74,925 written as 34 x 52 x 371?

What is prime factorization?

Prime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.

Finding the prime factors of 74,925

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.

If it doesn't make sense yet, let's try it...

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 74,925 by 2

74,925 ÷ 2 = 37,462.5 - This has a remainder. Let's try another prime number.
74,925 ÷ 3 = 24,975 - No remainder! 3 is one of the factors!
24,975 ÷ 3 = 8,325 - No remainder! 3 is one of the factors!
8,325 ÷ 3 = 2,775 - No remainder! 3 is one of the factors!
2,775 ÷ 3 = 925 - No remainder! 3 is one of the factors!
925 ÷ 3 = 308.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
925 ÷ 5 = 185 - No remainder! 5 is one of the factors!
185 ÷ 5 = 37 - No remainder! 5 is one of the factors!
37 ÷ 5 = 7.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
37 ÷ 7 = 5.2857 - This has a remainder. 7 is not a factor.
37 ÷ 11 = 3.3636 - This has a remainder. 11 is not a factor.
37 ÷ 13 = 2.8462 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
37 ÷ 37 = 1 - No remainder! 37 is one of the factors!

The orange divisor(s) above are the prime factors of the number 74,925. If we put all of it together we have the factors 3 x 3 x 3 x 3 x 5 x 5 x 37 = 74,925. It can also be written in exponential form as 34 x 52 x 371.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 74,925.

74,925
Factor Arrows
324,975
Factor Arrows
38,325
Factor Arrows
32,775
Factor Arrows
3925
Factor Arrows
5185
Factor Arrows
537

More Prime Factorization Examples

74,92374,92474,92674,927
74,923122 x 18,731121 x 37,4631311 x 2,4171

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