Q: What is the prime factorization of the number 130,355,810?

 A:
  • The prime factors are: 2 x 5 x 13 x 37 x 41 x 661
    • or also written as { 2, 5, 13, 37, 41, 661 }
  • Written in exponential form: 21 x 51 x 131 x 371 x 411 x 6611

Why is the prime factorization of 130,355,810 written as 21 x 51 x 131 x 371 x 411 x 6611?

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 130,355,810

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 130,355,810 by 2

130,355,810 ÷ 2 = 65,177,905 - No remainder! 2 is one of the factors!
65,177,905 ÷ 2 = 32,588,952.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
65,177,905 ÷ 3 = 21,725,968.3333 - This has a remainder. 3 is not a factor.
65,177,905 ÷ 5 = 13,035,581 - No remainder! 5 is one of the factors!
13,035,581 ÷ 5 = 2,607,116.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
13,035,581 ÷ 7 = 1,862,225.8571 - This has a remainder. 7 is not a factor.
13,035,581 ÷ 11 = 1,185,052.8182 - This has a remainder. 11 is not a factor.
13,035,581 ÷ 13 = 1,002,737 - No remainder! 13 is one of the factors!
1,002,737 ÷ 13 = 77,133.6154 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
1,002,737 ÷ 17 = 58,984.5294 - This has a remainder. 17 is not a factor.
1,002,737 ÷ 19 = 52,775.6316 - This has a remainder. 19 is not a factor.
1,002,737 ÷ 23 = 43,597.2609 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,002,737 ÷ 37 = 27,101 - No remainder! 37 is one of the factors!
27,101 ÷ 37 = 732.4595 - There is a remainder. We can't divide by 37 evenly anymore. Let's try the next prime number
27,101 ÷ 41 = 661 - No remainder! 41 is one of the factors!
661 ÷ 41 = 16.122 - There is a remainder. We can't divide by 41 evenly anymore. Let's try the next prime number
661 ÷ 43 = 15.3721 - This has a remainder. 43 is not a factor.
661 ÷ 47 = 14.0638 - This has a remainder. 47 is not a factor.
661 ÷ 53 = 12.4717 - This has a remainder. 53 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
661 ÷ 661 = 1 - No remainder! 661 is one of the factors!

The orange divisor(s) above are the prime factors of the number 130,355,810. If we put all of it together we have the factors 2 x 5 x 13 x 37 x 41 x 661 = 130,355,810. It can also be written in exponential form as 21 x 51 x 131 x 371 x 411 x 6611.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 130,355,810.

130,355,810
Factor Arrows
265,177,905
Factor Arrows
513,035,581
Factor Arrows
131,002,737
Factor Arrows
3727,101
Factor Arrows
41661

More Prime Factorization Examples

130,355,808130,355,809130,355,811130,355,812
25 x 31 x 111 x 191 x 731 x 891130,355,809134 x 2331 x 6,907122 x 231 x 291 x 48,8591

Try the factor calculator

Explore more about the number 130,355,810:


Ask a Question