Q: What is the prime factorization of the number 26,241,437?

 A:
  • The prime factors are: 211 x 124,367
    • or also written as { 211, 124,367 }
  • Written in exponential form: 2111 x 124,3671

Why is the prime factorization of 26,241,437 written as 2111 x 124,3671?

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 26,241,437

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 26,241,437 by 2

26,241,437 ÷ 2 = 13,120,718.5 - This has a remainder. Let's try another prime number.
26,241,437 ÷ 3 = 8,747,145.6667 - This has a remainder. Let's try another prime number.
26,241,437 ÷ 5 = 5,248,287.4 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
26,241,437 ÷ 211 = 124,367 - No remainder! 211 is one of the factors!
124,367 ÷ 211 = 589.4171 - There is a remainder. We can't divide by 211 evenly anymore. Let's try the next prime number
124,367 ÷ 223 = 557.6996 - This has a remainder. 223 is not a factor.
124,367 ÷ 227 = 547.8722 - This has a remainder. 227 is not a factor.
124,367 ÷ 229 = 543.0873 - This has a remainder. 229 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
124,367 ÷ 124,367 = 1 - No remainder! 124,367 is one of the factors!

The orange divisor(s) above are the prime factors of the number 26,241,437. If we put all of it together we have the factors 211 x 124,367 = 26,241,437. It can also be written in exponential form as 2111 x 124,3671.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 26,241,437.

26,241,437
Factor Arrows
211124,367

More Prime Factorization Examples

26,241,43526,241,43626,241,43826,241,439
33 x 51 x 111 x 411 x 431122 x 131 x 231 x 371 x 593121 x 31 x 171 x 311 x 431 x 193171 x 3071 x 12,2111

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