Q: What is the prime factorization of the number 26,053,440?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 3,877
    • or also written as { 2, 2, 2, 2, 2, 2, 3, 5, 7, 3,877 }
  • Written in exponential form: 26 x 31 x 51 x 71 x 3,8771

Why is the prime factorization of 26,053,440 written as 26 x 31 x 51 x 71 x 3,8771?

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 26,053,440

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 26,053,440 by 2

26,053,440 ÷ 2 = 13,026,720 - No remainder! 2 is one of the factors!
13,026,720 ÷ 2 = 6,513,360 - No remainder! 2 is one of the factors!
6,513,360 ÷ 2 = 3,256,680 - No remainder! 2 is one of the factors!
3,256,680 ÷ 2 = 1,628,340 - No remainder! 2 is one of the factors!
1,628,340 ÷ 2 = 814,170 - No remainder! 2 is one of the factors!
814,170 ÷ 2 = 407,085 - No remainder! 2 is one of the factors!
407,085 ÷ 2 = 203,542.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
407,085 ÷ 3 = 135,695 - No remainder! 3 is one of the factors!
135,695 ÷ 3 = 45,231.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
135,695 ÷ 5 = 27,139 - No remainder! 5 is one of the factors!
27,139 ÷ 5 = 5,427.8 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
27,139 ÷ 7 = 3,877 - No remainder! 7 is one of the factors!
3,877 ÷ 7 = 553.8571 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
3,877 ÷ 11 = 352.4545 - This has a remainder. 11 is not a factor.
3,877 ÷ 13 = 298.2308 - This has a remainder. 13 is not a factor.
3,877 ÷ 17 = 228.0588 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,877 ÷ 3,877 = 1 - No remainder! 3,877 is one of the factors!

The orange divisor(s) above are the prime factors of the number 26,053,440. 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 5 x 7 x 3,877 = 26,053,440. It can also be written in exponential form as 26 x 31 x 51 x 71 x 3,8771.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 26,053,440.

26,053,440
Factor Arrows
213,026,720
Factor Arrows
26,513,360
Factor Arrows
23,256,680
Factor Arrows
21,628,340
Factor Arrows
2814,170
Factor Arrows
2407,085
Factor Arrows
3135,695
Factor Arrows
527,139
Factor Arrows
73,877

More Prime Factorization Examples

26,053,43826,053,43926,053,44126,053,442
21 x 1031 x 126,4731372 x 19,031126,053,441121 x 431 x 4911 x 6171

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