Q: What is the prime factorization of the number 4,427,840?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 5 x 101 x 137
    • or also written as { 2, 2, 2, 2, 2, 2, 5, 101, 137 }
  • Written in exponential form: 26 x 51 x 1011 x 1371

Why is the prime factorization of 4,427,840 written as 26 x 51 x 1011 x 1371?

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 4,427,840

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 4,427,840 by 2

4,427,840 ÷ 2 = 2,213,920 - No remainder! 2 is one of the factors!
2,213,920 ÷ 2 = 1,106,960 - No remainder! 2 is one of the factors!
1,106,960 ÷ 2 = 553,480 - No remainder! 2 is one of the factors!
553,480 ÷ 2 = 276,740 - No remainder! 2 is one of the factors!
276,740 ÷ 2 = 138,370 - No remainder! 2 is one of the factors!
138,370 ÷ 2 = 69,185 - No remainder! 2 is one of the factors!
69,185 ÷ 2 = 34,592.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
69,185 ÷ 3 = 23,061.6667 - This has a remainder. 3 is not a factor.
69,185 ÷ 5 = 13,837 - No remainder! 5 is one of the factors!
13,837 ÷ 5 = 2,767.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
13,837 ÷ 7 = 1,976.7143 - This has a remainder. 7 is not a factor.
13,837 ÷ 11 = 1,257.9091 - This has a remainder. 11 is not a factor.
13,837 ÷ 13 = 1,064.3846 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
13,837 ÷ 101 = 137 - No remainder! 101 is one of the factors!
137 ÷ 101 = 1.3564 - There is a remainder. We can't divide by 101 evenly anymore. Let's try the next prime number
137 ÷ 103 = 1.3301 - This has a remainder. 103 is not a factor.
137 ÷ 107 = 1.2804 - This has a remainder. 107 is not a factor.
137 ÷ 109 = 1.2569 - This has a remainder. 109 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
137 ÷ 137 = 1 - No remainder! 137 is one of the factors!

The orange divisor(s) above are the prime factors of the number 4,427,840. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 5 x 101 x 137 = 4,427,840. It can also be written in exponential form as 26 x 51 x 1011 x 1371.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 4,427,840.

4,427,840
Factor Arrows
22,213,920
Factor Arrows
21,106,960
Factor Arrows
2553,480
Factor Arrows
2276,740
Factor Arrows
2138,370
Factor Arrows
269,185
Factor Arrows
513,837
Factor Arrows
101137

More Prime Factorization Examples

4,427,8384,427,8394,427,8414,427,842
21 x 33 x 1671 x 4911131 x 431 x 89231 x 111 x 134,177121 x 4011 x 5,5211

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