Q: What is the prime factorization of the number 877,492?

 A:
  • The prime factors are: 2 x 2 x 7 x 7 x 11 x 11 x 37
    • or also written as { 2, 2, 7, 7, 11, 11, 37 }
  • Written in exponential form: 22 x 72 x 112 x 371

Why is the prime factorization of 877,492 written as 22 x 72 x 112 x 371?

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 877,492

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 877,492 by 2

877,492 ÷ 2 = 438,746 - No remainder! 2 is one of the factors!
438,746 ÷ 2 = 219,373 - No remainder! 2 is one of the factors!
219,373 ÷ 2 = 109,686.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
219,373 ÷ 3 = 73,124.3333 - This has a remainder. 3 is not a factor.
219,373 ÷ 5 = 43,874.6 - This has a remainder. 5 is not a factor.
219,373 ÷ 7 = 31,339 - No remainder! 7 is one of the factors!
31,339 ÷ 7 = 4,477 - No remainder! 7 is one of the factors!
4,477 ÷ 7 = 639.5714 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
4,477 ÷ 11 = 407 - No remainder! 11 is one of the factors!
407 ÷ 11 = 37 - No remainder! 11 is one of the factors!
37 ÷ 11 = 3.3636 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
37 ÷ 13 = 2.8462 - This has a remainder. 13 is not a factor.
37 ÷ 17 = 2.1765 - This has a remainder. 17 is not a factor.
37 ÷ 19 = 1.9474 - This has a remainder. 19 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
37 ÷ 37 = 1 - No remainder! 37 is one of the factors!

The orange divisor(s) above are the prime factors of the number 877,492. If we put all of it together we have the factors 2 x 2 x 7 x 7 x 11 x 11 x 37 = 877,492. It can also be written in exponential form as 22 x 72 x 112 x 371.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 877,492.

877,492
Factor Arrows
2438,746
Factor Arrows
2219,373
Factor Arrows
731,339
Factor Arrows
74,477
Factor Arrows
11407
Factor Arrows
1137

More Prime Factorization Examples

877,490877,491877,493877,494
21 x 51 x 471 x 1,867132 x 97,49914671 x 1,879121 x 31 x 146,2491

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