Q: What is the prime factorization of the number 55,865,076?

 A:
  • The prime factors are: 2 x 2 x 3 x 661 x 7,043
    • or also written as { 2, 2, 3, 661, 7,043 }
  • Written in exponential form: 22 x 31 x 6611 x 7,0431

Why is the prime factorization of 55,865,076 written as 22 x 31 x 6611 x 7,0431?

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 55,865,076

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 55,865,076 by 2

55,865,076 ÷ 2 = 27,932,538 - No remainder! 2 is one of the factors!
27,932,538 ÷ 2 = 13,966,269 - No remainder! 2 is one of the factors!
13,966,269 ÷ 2 = 6,983,134.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
13,966,269 ÷ 3 = 4,655,423 - No remainder! 3 is one of the factors!
4,655,423 ÷ 3 = 1,551,807.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
4,655,423 ÷ 5 = 931,084.6 - This has a remainder. 5 is not a factor.
4,655,423 ÷ 7 = 665,060.4286 - This has a remainder. 7 is not a factor.
4,655,423 ÷ 11 = 423,220.2727 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
4,655,423 ÷ 661 = 7,043 - No remainder! 661 is one of the factors!
7,043 ÷ 661 = 10.6551 - There is a remainder. We can't divide by 661 evenly anymore. Let's try the next prime number
7,043 ÷ 673 = 10.4651 - This has a remainder. 673 is not a factor.
7,043 ÷ 677 = 10.4032 - This has a remainder. 677 is not a factor.
7,043 ÷ 683 = 10.3119 - This has a remainder. 683 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
7,043 ÷ 7,043 = 1 - No remainder! 7,043 is one of the factors!

The orange divisor(s) above are the prime factors of the number 55,865,076. If we put all of it together we have the factors 2 x 2 x 3 x 661 x 7,043 = 55,865,076. It can also be written in exponential form as 22 x 31 x 6611 x 7,0431.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 55,865,076.

55,865,076
Factor Arrows
227,932,538
Factor Arrows
213,966,269
Factor Arrows
34,655,423
Factor Arrows
6617,043

More Prime Factorization Examples

55,865,07455,865,07555,865,07755,865,078
21 x 531 x 3531 x 1,493152 x 71 x 731 x 4,3731171 x 3,286,181121 x 291 x 963,1911

Try the factor calculator

Explore more about the number 55,865,076:


Ask a Question