Q: What is the prime factorization of the number 7,434,240?

 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 3 x 5 x 11 x 11
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 11, 11 }
  • Written in exponential form: 212 x 31 x 51 x 112

Why is the prime factorization of 7,434,240 written as 212 x 31 x 51 x 112?

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 7,434,240

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 7,434,240 by 2

7,434,240 ÷ 2 = 3,717,120 - No remainder! 2 is one of the factors!
3,717,120 ÷ 2 = 1,858,560 - No remainder! 2 is one of the factors!
1,858,560 ÷ 2 = 929,280 - No remainder! 2 is one of the factors!
929,280 ÷ 2 = 464,640 - No remainder! 2 is one of the factors!
464,640 ÷ 2 = 232,320 - No remainder! 2 is one of the factors!
232,320 ÷ 2 = 116,160 - No remainder! 2 is one of the factors!
116,160 ÷ 2 = 58,080 - No remainder! 2 is one of the factors!
58,080 ÷ 2 = 29,040 - No remainder! 2 is one of the factors!
29,040 ÷ 2 = 14,520 - No remainder! 2 is one of the factors!
14,520 ÷ 2 = 7,260 - No remainder! 2 is one of the factors!
7,260 ÷ 2 = 3,630 - No remainder! 2 is one of the factors!
3,630 ÷ 2 = 1,815 - No remainder! 2 is one of the factors!
1,815 ÷ 2 = 907.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
1,815 ÷ 3 = 605 - No remainder! 3 is one of the factors!
605 ÷ 3 = 201.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
605 ÷ 5 = 121 - No remainder! 5 is one of the factors!
121 ÷ 5 = 24.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
121 ÷ 7 = 17.2857 - This has a remainder. 7 is not a factor.
121 ÷ 11 = 11 - No remainder! 11 is one of the factors!
11 ÷ 11 = 1 - No remainder! 11 is one of the factors!

The orange divisor(s) above are the prime factors of the number 7,434,240. 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 3 x 5 x 11 x 11 = 7,434,240. It can also be written in exponential form as 212 x 31 x 51 x 112.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 7,434,240.

7,434,240
Factor Arrows
23,717,120
Factor Arrows
21,858,560
Factor Arrows
2929,280
Factor Arrows
2464,640
Factor Arrows
2232,320
Factor Arrows
2116,160
Factor Arrows
258,080
Factor Arrows
229,040
Factor Arrows
214,520
Factor Arrows
27,260
Factor Arrows
23,630
Factor Arrows
21,815
Factor Arrows
3605
Factor Arrows
5121
Factor Arrows
1111

More Prime Factorization Examples

7,434,2387,434,2397,434,2417,434,242
21 x 71 x 531,01712571 x 28,92717,434,241121 x 1991 x 18,6791

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