Q: What is the prime factorization of the number 73,751,629?

 A:
  • The prime factors are: 7 x 383 x 27,509
    • or also written as { 7, 383, 27,509 }
  • Written in exponential form: 71 x 3831 x 27,5091

Why is the prime factorization of 73,751,629 written as 71 x 3831 x 27,5091?

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 73,751,629

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 73,751,629 by 2

73,751,629 ÷ 2 = 36,875,814.5 - This has a remainder. Let's try another prime number.
73,751,629 ÷ 3 = 24,583,876.3333 - This has a remainder. Let's try another prime number.
73,751,629 ÷ 5 = 14,750,325.8 - This has a remainder. Let's try another prime number.
73,751,629 ÷ 7 = 10,535,947 - No remainder! 7 is one of the factors!
10,535,947 ÷ 7 = 1,505,135.2857 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
10,535,947 ÷ 11 = 957,813.3636 - This has a remainder. 11 is not a factor.
10,535,947 ÷ 13 = 810,457.4615 - This has a remainder. 13 is not a factor.
10,535,947 ÷ 17 = 619,761.5882 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
10,535,947 ÷ 383 = 27,509 - No remainder! 383 is one of the factors!
27,509 ÷ 383 = 71.8251 - There is a remainder. We can't divide by 383 evenly anymore. Let's try the next prime number
27,509 ÷ 389 = 70.7172 - This has a remainder. 389 is not a factor.
27,509 ÷ 397 = 69.2922 - This has a remainder. 397 is not a factor.
27,509 ÷ 401 = 68.601 - This has a remainder. 401 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
27,509 ÷ 27,509 = 1 - No remainder! 27,509 is one of the factors!

The orange divisor(s) above are the prime factors of the number 73,751,629. If we put all of it together we have the factors 7 x 383 x 27,509 = 73,751,629. It can also be written in exponential form as 71 x 3831 x 27,5091.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 73,751,629.

73,751,629
Factor Arrows
710,535,947
Factor Arrows
38327,509

More Prime Factorization Examples

73,751,62773,751,62873,751,63073,751,631
171 x 4,338,331122 x 31 x 1,4391 x 4,271121 x 51 x 891 x 1731 x 479131 x 24,583,8771

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