Q: What is the prime factorization of the number 54,063,570?

 A:
  • The prime factors are: 2 x 3 x 5 x 11 x 17 x 23 x 419
    • or also written as { 2, 3, 5, 11, 17, 23, 419 }
  • Written in exponential form: 21 x 31 x 51 x 111 x 171 x 231 x 4191

Why is the prime factorization of 54,063,570 written as 21 x 31 x 51 x 111 x 171 x 231 x 4191?

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 54,063,570

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 54,063,570 by 2

54,063,570 ÷ 2 = 27,031,785 - No remainder! 2 is one of the factors!
27,031,785 ÷ 2 = 13,515,892.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
27,031,785 ÷ 3 = 9,010,595 - No remainder! 3 is one of the factors!
9,010,595 ÷ 3 = 3,003,531.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
9,010,595 ÷ 5 = 1,802,119 - No remainder! 5 is one of the factors!
1,802,119 ÷ 5 = 360,423.8 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
1,802,119 ÷ 7 = 257,445.5714 - This has a remainder. 7 is not a factor.
1,802,119 ÷ 11 = 163,829 - No remainder! 11 is one of the factors!
163,829 ÷ 11 = 14,893.5455 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
163,829 ÷ 13 = 12,602.2308 - This has a remainder. 13 is not a factor.
163,829 ÷ 17 = 9,637 - No remainder! 17 is one of the factors!
9,637 ÷ 17 = 566.8824 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
9,637 ÷ 19 = 507.2105 - This has a remainder. 19 is not a factor.
9,637 ÷ 23 = 419 - No remainder! 23 is one of the factors!
419 ÷ 23 = 18.2174 - There is a remainder. We can't divide by 23 evenly anymore. Let's try the next prime number
419 ÷ 29 = 14.4483 - This has a remainder. 29 is not a factor.
419 ÷ 31 = 13.5161 - This has a remainder. 31 is not a factor.
419 ÷ 37 = 11.3243 - This has a remainder. 37 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
419 ÷ 419 = 1 - No remainder! 419 is one of the factors!

The orange divisor(s) above are the prime factors of the number 54,063,570. If we put all of it together we have the factors 2 x 3 x 5 x 11 x 17 x 23 x 419 = 54,063,570. It can also be written in exponential form as 21 x 31 x 51 x 111 x 171 x 231 x 4191.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 54,063,570.

54,063,570
Factor Arrows
227,031,785
Factor Arrows
39,010,595
Factor Arrows
51,802,119
Factor Arrows
11163,829
Factor Arrows
179,637
Factor Arrows
23419

More Prime Factorization Examples

54,063,56854,063,56954,063,57154,063,572
24 x 131 x 611 x 4,261171 x 191 x 291 x 1071 x 1311791 x 684,349122 x 13,515,8931

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