Q: What is the prime factorization of the number 4,177,920?

 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 3 x 5 x 17
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 17 }
  • Written in exponential form: 214 x 31 x 51 x 171

Why is the prime factorization of 4,177,920 written as 214 x 31 x 51 x 171?

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 4,177,920

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 4,177,920 by 2

4,177,920 ÷ 2 = 2,088,960 - No remainder! 2 is one of the factors!
2,088,960 ÷ 2 = 1,044,480 - No remainder! 2 is one of the factors!
1,044,480 ÷ 2 = 522,240 - No remainder! 2 is one of the factors!
522,240 ÷ 2 = 261,120 - No remainder! 2 is one of the factors!
261,120 ÷ 2 = 130,560 - No remainder! 2 is one of the factors!
130,560 ÷ 2 = 65,280 - No remainder! 2 is one of the factors!
65,280 ÷ 2 = 32,640 - No remainder! 2 is one of the factors!
32,640 ÷ 2 = 16,320 - No remainder! 2 is one of the factors!
16,320 ÷ 2 = 8,160 - No remainder! 2 is one of the factors!
8,160 ÷ 2 = 4,080 - No remainder! 2 is one of the factors!
4,080 ÷ 2 = 2,040 - No remainder! 2 is one of the factors!
2,040 ÷ 2 = 1,020 - No remainder! 2 is one of the factors!
1,020 ÷ 2 = 510 - No remainder! 2 is one of the factors!
510 ÷ 2 = 255 - No remainder! 2 is one of the factors!
255 ÷ 2 = 127.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
255 ÷ 3 = 85 - No remainder! 3 is one of the factors!
85 ÷ 3 = 28.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
85 ÷ 5 = 17 - No remainder! 5 is one of the factors!
17 ÷ 5 = 3.4 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
17 ÷ 7 = 2.4286 - This has a remainder. 7 is not a factor.
17 ÷ 11 = 1.5455 - This has a remainder. 11 is not a factor.
17 ÷ 13 = 1.3077 - This has a remainder. 13 is not a factor.
17 ÷ 17 = 1 - No remainder! 17 is one of the factors!

The orange divisor(s) above are the prime factors of the number 4,177,920. 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 3 x 5 x 17 = 4,177,920. It can also be written in exponential form as 214 x 31 x 51 x 171.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 4,177,920.

4,177,920
Factor Arrows
22,088,960
Factor Arrows
21,044,480
Factor Arrows
2522,240
Factor Arrows
2261,120
Factor Arrows
2130,560
Factor Arrows
265,280
Factor Arrows
232,640
Factor Arrows
216,320
Factor Arrows
28,160
Factor Arrows
24,080
Factor Arrows
22,040
Factor Arrows
21,020
Factor Arrows
2510
Factor Arrows
2255
Factor Arrows
385
Factor Arrows
517

More Prime Factorization Examples

4,177,9184,177,9194,177,9214,177,922
21 x 5031 x 4,1531671 x 1271 x 4911111 x 379,811121 x 71 x 1071 x 2,7891

Try the factor calculator

Explore more about the number 4,177,920:


Ask a Question