Q: What is the prime factorization of the number 4,622,976?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 4,013
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 3, 3, 4,013 }
  • Written in exponential form: 27 x 32 x 4,0131

Why is the prime factorization of 4,622,976 written as 27 x 32 x 4,0131?

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 4,622,976

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 4,622,976 by 2

4,622,976 ÷ 2 = 2,311,488 - No remainder! 2 is one of the factors!
2,311,488 ÷ 2 = 1,155,744 - No remainder! 2 is one of the factors!
1,155,744 ÷ 2 = 577,872 - No remainder! 2 is one of the factors!
577,872 ÷ 2 = 288,936 - No remainder! 2 is one of the factors!
288,936 ÷ 2 = 144,468 - No remainder! 2 is one of the factors!
144,468 ÷ 2 = 72,234 - No remainder! 2 is one of the factors!
72,234 ÷ 2 = 36,117 - No remainder! 2 is one of the factors!
36,117 ÷ 2 = 18,058.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
36,117 ÷ 3 = 12,039 - No remainder! 3 is one of the factors!
12,039 ÷ 3 = 4,013 - No remainder! 3 is one of the factors!
4,013 ÷ 3 = 1,337.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
4,013 ÷ 5 = 802.6 - This has a remainder. 5 is not a factor.
4,013 ÷ 7 = 573.2857 - This has a remainder. 7 is not a factor.
4,013 ÷ 11 = 364.8182 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
4,013 ÷ 4,013 = 1 - No remainder! 4,013 is one of the factors!

The orange divisor(s) above are the prime factors of the number 4,622,976. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 4,013 = 4,622,976. It can also be written in exponential form as 27 x 32 x 4,0131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 4,622,976.

4,622,976
Factor Arrows
22,311,488
Factor Arrows
21,155,744
Factor Arrows
2577,872
Factor Arrows
2288,936
Factor Arrows
2144,468
Factor Arrows
272,234
Factor Arrows
236,117
Factor Arrows
312,039
Factor Arrows
34,013

More Prime Factorization Examples

4,622,9744,622,9754,622,9774,622,978
21 x 2,311,487152 x 71 x 26,4171231 x 292 x 239121 x 531 x 43,6131

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