Q: What is the prime factorization of the number 93,470,720?

 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 2 x 2 x 2 x 5 x 7 x 163
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7, 163 }
  • Written in exponential form: 214 x 51 x 71 x 1631

Why is the prime factorization of 93,470,720 written as 214 x 51 x 71 x 1631?

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 93,470,720

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 93,470,720 by 2

93,470,720 ÷ 2 = 46,735,360 - No remainder! 2 is one of the factors!
46,735,360 ÷ 2 = 23,367,680 - No remainder! 2 is one of the factors!
23,367,680 ÷ 2 = 11,683,840 - No remainder! 2 is one of the factors!
11,683,840 ÷ 2 = 5,841,920 - No remainder! 2 is one of the factors!
5,841,920 ÷ 2 = 2,920,960 - No remainder! 2 is one of the factors!
2,920,960 ÷ 2 = 1,460,480 - No remainder! 2 is one of the factors!
1,460,480 ÷ 2 = 730,240 - No remainder! 2 is one of the factors!
730,240 ÷ 2 = 365,120 - No remainder! 2 is one of the factors!
365,120 ÷ 2 = 182,560 - No remainder! 2 is one of the factors!
182,560 ÷ 2 = 91,280 - No remainder! 2 is one of the factors!
91,280 ÷ 2 = 45,640 - No remainder! 2 is one of the factors!
45,640 ÷ 2 = 22,820 - No remainder! 2 is one of the factors!
22,820 ÷ 2 = 11,410 - No remainder! 2 is one of the factors!
11,410 ÷ 2 = 5,705 - No remainder! 2 is one of the factors!
5,705 ÷ 2 = 2,852.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
5,705 ÷ 3 = 1,901.6667 - This has a remainder. 3 is not a factor.
5,705 ÷ 5 = 1,141 - No remainder! 5 is one of the factors!
1,141 ÷ 5 = 228.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
1,141 ÷ 7 = 163 - No remainder! 7 is one of the factors!
163 ÷ 7 = 23.2857 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
163 ÷ 11 = 14.8182 - This has a remainder. 11 is not a factor.
163 ÷ 13 = 12.5385 - This has a remainder. 13 is not a factor.
163 ÷ 17 = 9.5882 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
163 ÷ 163 = 1 - No remainder! 163 is one of the factors!

The orange divisor(s) above are the prime factors of the number 93,470,720. 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 2 x 2 x 2 x 5 x 7 x 163 = 93,470,720. It can also be written in exponential form as 214 x 51 x 71 x 1631.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 93,470,720.

93,470,720
Factor Arrows
246,735,360
Factor Arrows
223,367,680
Factor Arrows
211,683,840
Factor Arrows
25,841,920
Factor Arrows
22,920,960
Factor Arrows
21,460,480
Factor Arrows
2730,240
Factor Arrows
2365,120
Factor Arrows
2182,560
Factor Arrows
291,280
Factor Arrows
245,640
Factor Arrows
222,820
Factor Arrows
211,410
Factor Arrows
25,705
Factor Arrows
51,141
Factor Arrows
7163

More Prime Factorization Examples

93,470,71893,470,71993,470,72193,470,722
21 x 31 x 111 x 1,416,2231711 x 7191 x 1,831131 x 4,3571 x 7,151121 x 46,735,3611

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