Q: What is the prime factorization of the number 110,041,007?

 A:
  • The prime factors are: 41 x 233 x 11,519
    • or also written as { 41, 233, 11,519 }
  • Written in exponential form: 411 x 2331 x 11,5191

Why is the prime factorization of 110,041,007 written as 411 x 2331 x 11,5191?

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 110,041,007

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 110,041,007 by 2

110,041,007 ÷ 2 = 55,020,503.5 - This has a remainder. Let's try another prime number.
110,041,007 ÷ 3 = 36,680,335.6667 - This has a remainder. Let's try another prime number.
110,041,007 ÷ 5 = 22,008,201.4 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
110,041,007 ÷ 41 = 2,683,927 - No remainder! 41 is one of the factors!
2,683,927 ÷ 41 = 65,461.6341 - There is a remainder. We can't divide by 41 evenly anymore. Let's try the next prime number
2,683,927 ÷ 43 = 62,416.907 - This has a remainder. 43 is not a factor.
2,683,927 ÷ 47 = 57,104.8298 - This has a remainder. 47 is not a factor.
2,683,927 ÷ 53 = 50,640.1321 - This has a remainder. 53 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,683,927 ÷ 233 = 11,519 - No remainder! 233 is one of the factors!
11,519 ÷ 233 = 49.4378 - There is a remainder. We can't divide by 233 evenly anymore. Let's try the next prime number
11,519 ÷ 239 = 48.1967 - This has a remainder. 239 is not a factor.
11,519 ÷ 241 = 47.7967 - This has a remainder. 241 is not a factor.
11,519 ÷ 251 = 45.8924 - This has a remainder. 251 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
11,519 ÷ 11,519 = 1 - No remainder! 11,519 is one of the factors!

The orange divisor(s) above are the prime factors of the number 110,041,007. If we put all of it together we have the factors 41 x 233 x 11,519 = 110,041,007. It can also be written in exponential form as 411 x 2331 x 11,5191.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 110,041,007.

110,041,007
Factor Arrows
412,683,927
Factor Arrows
23311,519

More Prime Factorization Examples

110,041,005110,041,006110,041,008110,041,009
31 x 51 x 2811 x 26,107121 x 471 x 1,170,649124 x 31 x 71 x 111 x 191 x 1,5671131 x 8,464,6931

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