Q: What is the prime factorization of the number 63,641,342?

 A:
  • The prime factors are: 2 x 883 x 36,037
    • or also written as { 2, 883, 36,037 }
  • Written in exponential form: 21 x 8831 x 36,0371

Why is the prime factorization of 63,641,342 written as 21 x 8831 x 36,0371?

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 63,641,342

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 63,641,342 by 2

63,641,342 ÷ 2 = 31,820,671 - No remainder! 2 is one of the factors!
31,820,671 ÷ 2 = 15,910,335.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
31,820,671 ÷ 3 = 10,606,890.3333 - This has a remainder. 3 is not a factor.
31,820,671 ÷ 5 = 6,364,134.2 - This has a remainder. 5 is not a factor.
31,820,671 ÷ 7 = 4,545,810.1429 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
31,820,671 ÷ 883 = 36,037 - No remainder! 883 is one of the factors!
36,037 ÷ 883 = 40.812 - There is a remainder. We can't divide by 883 evenly anymore. Let's try the next prime number
36,037 ÷ 887 = 40.628 - This has a remainder. 887 is not a factor.
36,037 ÷ 907 = 39.7321 - This has a remainder. 907 is not a factor.
36,037 ÷ 911 = 39.5576 - This has a remainder. 911 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
36,037 ÷ 36,037 = 1 - No remainder! 36,037 is one of the factors!

The orange divisor(s) above are the prime factors of the number 63,641,342. If we put all of it together we have the factors 2 x 883 x 36,037 = 63,641,342. It can also be written in exponential form as 21 x 8831 x 36,0371.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 63,641,342.

63,641,342
Factor Arrows
231,820,671
Factor Arrows
88336,037

More Prime Factorization Examples

63,641,34063,641,34163,641,34363,641,344
22 x 32 x 51 x 71 x 531 x 9531291 x 2,194,529131 x 21,213,781128 x 132 x 1,4711

Try the factor calculator

Explore more about the number 63,641,342:


Ask a Question