Q: What is the prime factorization of the number 4,967,424?

 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 3 x 3 x 7 x 7 x 11
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 7, 11 }
  • Written in exponential form: 210 x 32 x 72 x 111

Why is the prime factorization of 4,967,424 written as 210 x 32 x 72 x 111?

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 4,967,424

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 4,967,424 by 2

4,967,424 ÷ 2 = 2,483,712 - No remainder! 2 is one of the factors!
2,483,712 ÷ 2 = 1,241,856 - No remainder! 2 is one of the factors!
1,241,856 ÷ 2 = 620,928 - No remainder! 2 is one of the factors!
620,928 ÷ 2 = 310,464 - No remainder! 2 is one of the factors!
310,464 ÷ 2 = 155,232 - No remainder! 2 is one of the factors!
155,232 ÷ 2 = 77,616 - No remainder! 2 is one of the factors!
77,616 ÷ 2 = 38,808 - No remainder! 2 is one of the factors!
38,808 ÷ 2 = 19,404 - No remainder! 2 is one of the factors!
19,404 ÷ 2 = 9,702 - No remainder! 2 is one of the factors!
9,702 ÷ 2 = 4,851 - No remainder! 2 is one of the factors!
4,851 ÷ 2 = 2,425.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
4,851 ÷ 3 = 1,617 - No remainder! 3 is one of the factors!
1,617 ÷ 3 = 539 - No remainder! 3 is one of the factors!
539 ÷ 3 = 179.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
539 ÷ 5 = 107.8 - This has a remainder. 5 is not a factor.
539 ÷ 7 = 77 - No remainder! 7 is one of the factors!
77 ÷ 7 = 11 - No remainder! 7 is one of the factors!
11 ÷ 7 = 1.5714 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
11 ÷ 11 = 1 - No remainder! 11 is one of the factors!

The orange divisor(s) above are the prime factors of the number 4,967,424. 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 3 x 3 x 7 x 7 x 11 = 4,967,424. It can also be written in exponential form as 210 x 32 x 72 x 111.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 4,967,424.

4,967,424
Factor Arrows
22,483,712
Factor Arrows
21,241,856
Factor Arrows
2620,928
Factor Arrows
2310,464
Factor Arrows
2155,232
Factor Arrows
277,616
Factor Arrows
238,808
Factor Arrows
219,404
Factor Arrows
29,702
Factor Arrows
24,851
Factor Arrows
31,617
Factor Arrows
3539
Factor Arrows
777
Factor Arrows
711

More Prime Factorization Examples

4,967,4224,967,4234,967,4254,967,426
21 x 2,483,71114,967,423152 x 231 x 531 x 163121 x 2,483,7131

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