Q: What is the prime factorization of the number 101,067,776?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 229 x 431
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 229, 431 }
  • Written in exponential form: 210 x 2291 x 4311

Why is the prime factorization of 101,067,776 written as 210 x 2291 x 4311?

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 101,067,776

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 101,067,776 by 2

101,067,776 ÷ 2 = 50,533,888 - No remainder! 2 is one of the factors!
50,533,888 ÷ 2 = 25,266,944 - No remainder! 2 is one of the factors!
25,266,944 ÷ 2 = 12,633,472 - No remainder! 2 is one of the factors!
12,633,472 ÷ 2 = 6,316,736 - No remainder! 2 is one of the factors!
6,316,736 ÷ 2 = 3,158,368 - No remainder! 2 is one of the factors!
3,158,368 ÷ 2 = 1,579,184 - No remainder! 2 is one of the factors!
1,579,184 ÷ 2 = 789,592 - No remainder! 2 is one of the factors!
789,592 ÷ 2 = 394,796 - No remainder! 2 is one of the factors!
394,796 ÷ 2 = 197,398 - No remainder! 2 is one of the factors!
197,398 ÷ 2 = 98,699 - No remainder! 2 is one of the factors!
98,699 ÷ 2 = 49,349.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
98,699 ÷ 3 = 32,899.6667 - This has a remainder. 3 is not a factor.
98,699 ÷ 5 = 19,739.8 - This has a remainder. 5 is not a factor.
98,699 ÷ 7 = 14,099.8571 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
98,699 ÷ 229 = 431 - No remainder! 229 is one of the factors!
431 ÷ 229 = 1.8821 - There is a remainder. We can't divide by 229 evenly anymore. Let's try the next prime number
431 ÷ 233 = 1.8498 - This has a remainder. 233 is not a factor.
431 ÷ 239 = 1.8033 - This has a remainder. 239 is not a factor.
431 ÷ 241 = 1.7884 - This has a remainder. 241 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
431 ÷ 431 = 1 - No remainder! 431 is one of the factors!

The orange divisor(s) above are the prime factors of the number 101,067,776. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 229 x 431 = 101,067,776. It can also be written in exponential form as 210 x 2291 x 4311.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 101,067,776.

101,067,776
Factor Arrows
250,533,888
Factor Arrows
225,266,944
Factor Arrows
212,633,472
Factor Arrows
26,316,736
Factor Arrows
23,158,368
Factor Arrows
21,579,184
Factor Arrows
2789,592
Factor Arrows
2394,796
Factor Arrows
2197,398
Factor Arrows
298,699
Factor Arrows
229431

More Prime Factorization Examples

101,067,774101,067,775101,067,777101,067,778
21 x 31 x 1,4531 x 11,593152 x 6731 x 6,007133 x 891 x 1371 x 307121 x 71 x 1,3671 x 5,2811

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