Q: What is the prime factorization of the number 14,377,152?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 103 x 727
    • or also written as { 2, 2, 2, 2, 2, 2, 3, 103, 727 }
  • Written in exponential form: 26 x 31 x 1031 x 7271

Why is the prime factorization of 14,377,152 written as 26 x 31 x 1031 x 7271?

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 14,377,152

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 14,377,152 by 2

14,377,152 ÷ 2 = 7,188,576 - No remainder! 2 is one of the factors!
7,188,576 ÷ 2 = 3,594,288 - No remainder! 2 is one of the factors!
3,594,288 ÷ 2 = 1,797,144 - No remainder! 2 is one of the factors!
1,797,144 ÷ 2 = 898,572 - No remainder! 2 is one of the factors!
898,572 ÷ 2 = 449,286 - No remainder! 2 is one of the factors!
449,286 ÷ 2 = 224,643 - No remainder! 2 is one of the factors!
224,643 ÷ 2 = 112,321.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
224,643 ÷ 3 = 74,881 - No remainder! 3 is one of the factors!
74,881 ÷ 3 = 24,960.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
74,881 ÷ 5 = 14,976.2 - This has a remainder. 5 is not a factor.
74,881 ÷ 7 = 10,697.2857 - This has a remainder. 7 is not a factor.
74,881 ÷ 11 = 6,807.3636 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
74,881 ÷ 103 = 727 - No remainder! 103 is one of the factors!
727 ÷ 103 = 7.0583 - There is a remainder. We can't divide by 103 evenly anymore. Let's try the next prime number
727 ÷ 107 = 6.7944 - This has a remainder. 107 is not a factor.
727 ÷ 109 = 6.6697 - This has a remainder. 109 is not a factor.
727 ÷ 113 = 6.4336 - This has a remainder. 113 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
727 ÷ 727 = 1 - No remainder! 727 is one of the factors!

The orange divisor(s) above are the prime factors of the number 14,377,152. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 3 x 103 x 727 = 14,377,152. It can also be written in exponential form as 26 x 31 x 1031 x 7271.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 14,377,152.

14,377,152
Factor Arrows
27,188,576
Factor Arrows
23,594,288
Factor Arrows
21,797,144
Factor Arrows
2898,572
Factor Arrows
2449,286
Factor Arrows
2224,643
Factor Arrows
374,881
Factor Arrows
103727

More Prime Factorization Examples

14,377,15014,377,15114,377,15314,377,154
21 x 52 x 4211 x 6831531 x 611 x 4,447171 x 1991 x 10,321121 x 111 x 653,5071

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