Q: What is the prime factorization of the number 2,772,620?

 A:
  • The prime factors are: 2 x 2 x 5 x 157 x 883
    • or also written as { 2, 2, 5, 157, 883 }
  • Written in exponential form: 22 x 51 x 1571 x 8831

Why is the prime factorization of 2,772,620 written as 22 x 51 x 1571 x 8831?

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 2,772,620

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 2,772,620 by 2

2,772,620 ÷ 2 = 1,386,310 - No remainder! 2 is one of the factors!
1,386,310 ÷ 2 = 693,155 - No remainder! 2 is one of the factors!
693,155 ÷ 2 = 346,577.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
693,155 ÷ 3 = 231,051.6667 - This has a remainder. 3 is not a factor.
693,155 ÷ 5 = 138,631 - No remainder! 5 is one of the factors!
138,631 ÷ 5 = 27,726.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
138,631 ÷ 7 = 19,804.4286 - This has a remainder. 7 is not a factor.
138,631 ÷ 11 = 12,602.8182 - This has a remainder. 11 is not a factor.
138,631 ÷ 13 = 10,663.9231 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
138,631 ÷ 157 = 883 - No remainder! 157 is one of the factors!
883 ÷ 157 = 5.6242 - There is a remainder. We can't divide by 157 evenly anymore. Let's try the next prime number
883 ÷ 163 = 5.4172 - This has a remainder. 163 is not a factor.
883 ÷ 167 = 5.2874 - This has a remainder. 167 is not a factor.
883 ÷ 173 = 5.104 - This has a remainder. 173 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
883 ÷ 883 = 1 - No remainder! 883 is one of the factors!

The orange divisor(s) above are the prime factors of the number 2,772,620. If we put all of it together we have the factors 2 x 2 x 5 x 157 x 883 = 2,772,620. It can also be written in exponential form as 22 x 51 x 1571 x 8831.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 2,772,620.

2,772,620
Factor Arrows
21,386,310
Factor Arrows
2693,155
Factor Arrows
5138,631
Factor Arrows
157883

More Prime Factorization Examples

2,772,6182,772,6192,772,6212,772,622
21 x 31 x 462,10314571 x 6,067132 x 711 x 4,339121 x 1,386,3111

Try the factor calculator

Explore more about the number 2,772,620:


Ask a Question