Q: What is the prime factorization of the number 177,424,620?

 A:
  • The prime factors are: 2 x 2 x 3 x 5 x 37 x 229 x 349
    • or also written as { 2, 2, 3, 5, 37, 229, 349 }
  • Written in exponential form: 22 x 31 x 51 x 371 x 2291 x 3491

Why is the prime factorization of 177,424,620 written as 22 x 31 x 51 x 371 x 2291 x 3491?

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 177,424,620

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 177,424,620 by 2

177,424,620 ÷ 2 = 88,712,310 - No remainder! 2 is one of the factors!
88,712,310 ÷ 2 = 44,356,155 - No remainder! 2 is one of the factors!
44,356,155 ÷ 2 = 22,178,077.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
44,356,155 ÷ 3 = 14,785,385 - No remainder! 3 is one of the factors!
14,785,385 ÷ 3 = 4,928,461.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
14,785,385 ÷ 5 = 2,957,077 - No remainder! 5 is one of the factors!
2,957,077 ÷ 5 = 591,415.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
2,957,077 ÷ 7 = 422,439.5714 - This has a remainder. 7 is not a factor.
2,957,077 ÷ 11 = 268,825.1818 - This has a remainder. 11 is not a factor.
2,957,077 ÷ 13 = 227,467.4615 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,957,077 ÷ 37 = 79,921 - No remainder! 37 is one of the factors!
79,921 ÷ 37 = 2,160.027 - There is a remainder. We can't divide by 37 evenly anymore. Let's try the next prime number
79,921 ÷ 41 = 1,949.2927 - This has a remainder. 41 is not a factor.
79,921 ÷ 43 = 1,858.6279 - This has a remainder. 43 is not a factor.
79,921 ÷ 47 = 1,700.4468 - This has a remainder. 47 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
79,921 ÷ 229 = 349 - No remainder! 229 is one of the factors!
349 ÷ 229 = 1.524 - There is a remainder. We can't divide by 229 evenly anymore. Let's try the next prime number
349 ÷ 233 = 1.4979 - This has a remainder. 233 is not a factor.
349 ÷ 239 = 1.4603 - This has a remainder. 239 is not a factor.
349 ÷ 241 = 1.4481 - This has a remainder. 241 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
349 ÷ 349 = 1 - No remainder! 349 is one of the factors!

The orange divisor(s) above are the prime factors of the number 177,424,620. If we put all of it together we have the factors 2 x 2 x 3 x 5 x 37 x 229 x 349 = 177,424,620. It can also be written in exponential form as 22 x 31 x 51 x 371 x 2291 x 3491.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 177,424,620.

177,424,620
Factor Arrows
288,712,310
Factor Arrows
244,356,155
Factor Arrows
314,785,385
Factor Arrows
52,957,077
Factor Arrows
3779,921
Factor Arrows
229349

More Prime Factorization Examples

177,424,618177,424,619177,424,621177,424,622
21 x 71 x 831 x 1071 x 1,42711991 x 9071 x 9831111 x 1791 x 2511 x 359121 x 191 x 231 x 431 x 4,7211

Try the factor calculator

Explore more about the number 177,424,620:


Ask a Question