Q: What is the prime factorization of the number 4,630,528?

 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 2 x 7 x 17 x 19
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 17, 19 }
  • Written in exponential form: 211 x 71 x 171 x 191

Why is the prime factorization of 4,630,528 written as 211 x 71 x 171 x 191?

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 4,630,528

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 4,630,528 by 2

4,630,528 ÷ 2 = 2,315,264 - No remainder! 2 is one of the factors!
2,315,264 ÷ 2 = 1,157,632 - No remainder! 2 is one of the factors!
1,157,632 ÷ 2 = 578,816 - No remainder! 2 is one of the factors!
578,816 ÷ 2 = 289,408 - No remainder! 2 is one of the factors!
289,408 ÷ 2 = 144,704 - No remainder! 2 is one of the factors!
144,704 ÷ 2 = 72,352 - No remainder! 2 is one of the factors!
72,352 ÷ 2 = 36,176 - No remainder! 2 is one of the factors!
36,176 ÷ 2 = 18,088 - No remainder! 2 is one of the factors!
18,088 ÷ 2 = 9,044 - No remainder! 2 is one of the factors!
9,044 ÷ 2 = 4,522 - No remainder! 2 is one of the factors!
4,522 ÷ 2 = 2,261 - No remainder! 2 is one of the factors!
2,261 ÷ 2 = 1,130.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
2,261 ÷ 3 = 753.6667 - This has a remainder. 3 is not a factor.
2,261 ÷ 5 = 452.2 - This has a remainder. 5 is not a factor.
2,261 ÷ 7 = 323 - No remainder! 7 is one of the factors!
323 ÷ 7 = 46.1429 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
323 ÷ 11 = 29.3636 - This has a remainder. 11 is not a factor.
323 ÷ 13 = 24.8462 - This has a remainder. 13 is not a factor.
323 ÷ 17 = 19 - No remainder! 17 is one of the factors!
19 ÷ 17 = 1.1176 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
19 ÷ 19 = 1 - No remainder! 19 is one of the factors!

The orange divisor(s) above are the prime factors of the number 4,630,528. 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 2 x 7 x 17 x 19 = 4,630,528. It can also be written in exponential form as 211 x 71 x 171 x 191.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 4,630,528.

4,630,528
Factor Arrows
22,315,264
Factor Arrows
21,157,632
Factor Arrows
2578,816
Factor Arrows
2289,408
Factor Arrows
2144,704
Factor Arrows
272,352
Factor Arrows
236,176
Factor Arrows
218,088
Factor Arrows
29,044
Factor Arrows
24,522
Factor Arrows
22,261
Factor Arrows
7323
Factor Arrows
1719

More Prime Factorization Examples

4,630,5264,630,5274,630,5294,630,530
21 x 2,315,263134 x 111 x 5,19714,630,529121 x 31 x 51 x 154,3511

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