Q: What is the prime factorization of the number 146,007,276?

 A:
  • The prime factors are: 2 x 2 x 3 x 191 x 63,703
    • or also written as { 2, 2, 3, 191, 63,703 }
  • Written in exponential form: 22 x 31 x 1911 x 63,7031

Why is the prime factorization of 146,007,276 written as 22 x 31 x 1911 x 63,7031?

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 146,007,276

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 146,007,276 by 2

146,007,276 ÷ 2 = 73,003,638 - No remainder! 2 is one of the factors!
73,003,638 ÷ 2 = 36,501,819 - No remainder! 2 is one of the factors!
36,501,819 ÷ 2 = 18,250,909.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
36,501,819 ÷ 3 = 12,167,273 - No remainder! 3 is one of the factors!
12,167,273 ÷ 3 = 4,055,757.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
12,167,273 ÷ 5 = 2,433,454.6 - This has a remainder. 5 is not a factor.
12,167,273 ÷ 7 = 1,738,181.8571 - This has a remainder. 7 is not a factor.
12,167,273 ÷ 11 = 1,106,115.7273 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
12,167,273 ÷ 191 = 63,703 - No remainder! 191 is one of the factors!
63,703 ÷ 191 = 333.5236 - There is a remainder. We can't divide by 191 evenly anymore. Let's try the next prime number
63,703 ÷ 193 = 330.0674 - This has a remainder. 193 is not a factor.
63,703 ÷ 197 = 323.3655 - This has a remainder. 197 is not a factor.
63,703 ÷ 199 = 320.1156 - This has a remainder. 199 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
63,703 ÷ 63,703 = 1 - No remainder! 63,703 is one of the factors!

The orange divisor(s) above are the prime factors of the number 146,007,276. If we put all of it together we have the factors 2 x 2 x 3 x 191 x 63,703 = 146,007,276. It can also be written in exponential form as 22 x 31 x 1911 x 63,7031.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 146,007,276.

146,007,276
Factor Arrows
273,003,638
Factor Arrows
236,501,819
Factor Arrows
312,167,273
Factor Arrows
19163,703

More Prime Factorization Examples

146,007,274146,007,275146,007,277146,007,278
21 x 71 x 431 x 4091 x 593152 x 5,840,2911131 x 11,231,329121 x 1071 x 682,2771

Try the factor calculator

Explore more about the number 146,007,276:


Ask a Question