Q: What is the prime factorization of the number 61,004,347?

 A:
  • The prime factors are: 17 x 257 x 13,963
    • or also written as { 17, 257, 13,963 }
  • Written in exponential form: 171 x 2571 x 13,9631

Why is the prime factorization of 61,004,347 written as 171 x 2571 x 13,9631?

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 61,004,347

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 61,004,347 by 2

61,004,347 ÷ 2 = 30,502,173.5 - This has a remainder. Let's try another prime number.
61,004,347 ÷ 3 = 20,334,782.3333 - This has a remainder. Let's try another prime number.
61,004,347 ÷ 5 = 12,200,869.4 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
61,004,347 ÷ 17 = 3,588,491 - No remainder! 17 is one of the factors!
3,588,491 ÷ 17 = 211,087.7059 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
3,588,491 ÷ 19 = 188,867.9474 - This has a remainder. 19 is not a factor.
3,588,491 ÷ 23 = 156,021.3478 - This has a remainder. 23 is not a factor.
3,588,491 ÷ 29 = 123,741.069 - This has a remainder. 29 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,588,491 ÷ 257 = 13,963 - No remainder! 257 is one of the factors!
13,963 ÷ 257 = 54.3307 - There is a remainder. We can't divide by 257 evenly anymore. Let's try the next prime number
13,963 ÷ 263 = 53.0913 - This has a remainder. 263 is not a factor.
13,963 ÷ 269 = 51.9071 - This has a remainder. 269 is not a factor.
13,963 ÷ 271 = 51.524 - This has a remainder. 271 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
13,963 ÷ 13,963 = 1 - No remainder! 13,963 is one of the factors!

The orange divisor(s) above are the prime factors of the number 61,004,347. If we put all of it together we have the factors 17 x 257 x 13,963 = 61,004,347. It can also be written in exponential form as 171 x 2571 x 13,9631.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 61,004,347.

61,004,347
Factor Arrows
173,588,491
Factor Arrows
25713,963

More Prime Factorization Examples

61,004,34561,004,34661,004,34861,004,349
51 x 191 x 642,151121 x 31 x 131 x 782,107122 x 591 x 731 x 3,541132 x 71 x 231 x 42,1011

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