Q: What is the prime factorization of the number 64,450,560?

 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 1,049
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 1,049 }
  • Written in exponential form: 212 x 31 x 51 x 1,0491

Why is the prime factorization of 64,450,560 written as 212 x 31 x 51 x 1,0491?

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 64,450,560

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 64,450,560 by 2

64,450,560 ÷ 2 = 32,225,280 - No remainder! 2 is one of the factors!
32,225,280 ÷ 2 = 16,112,640 - No remainder! 2 is one of the factors!
16,112,640 ÷ 2 = 8,056,320 - No remainder! 2 is one of the factors!
8,056,320 ÷ 2 = 4,028,160 - No remainder! 2 is one of the factors!
4,028,160 ÷ 2 = 2,014,080 - No remainder! 2 is one of the factors!
2,014,080 ÷ 2 = 1,007,040 - No remainder! 2 is one of the factors!
1,007,040 ÷ 2 = 503,520 - No remainder! 2 is one of the factors!
503,520 ÷ 2 = 251,760 - No remainder! 2 is one of the factors!
251,760 ÷ 2 = 125,880 - No remainder! 2 is one of the factors!
125,880 ÷ 2 = 62,940 - No remainder! 2 is one of the factors!
62,940 ÷ 2 = 31,470 - No remainder! 2 is one of the factors!
31,470 ÷ 2 = 15,735 - No remainder! 2 is one of the factors!
15,735 ÷ 2 = 7,867.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
15,735 ÷ 3 = 5,245 - No remainder! 3 is one of the factors!
5,245 ÷ 3 = 1,748.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
5,245 ÷ 5 = 1,049 - No remainder! 5 is one of the factors!
1,049 ÷ 5 = 209.8 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
1,049 ÷ 7 = 149.8571 - This has a remainder. 7 is not a factor.
1,049 ÷ 11 = 95.3636 - This has a remainder. 11 is not a factor.
1,049 ÷ 13 = 80.6923 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,049 ÷ 1,049 = 1 - No remainder! 1,049 is one of the factors!

The orange divisor(s) above are the prime factors of the number 64,450,560. 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 1,049 = 64,450,560. It can also be written in exponential form as 212 x 31 x 51 x 1,0491.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 64,450,560.

64,450,560
Factor Arrows
232,225,280
Factor Arrows
216,112,640
Factor Arrows
28,056,320
Factor Arrows
24,028,160
Factor Arrows
22,014,080
Factor Arrows
21,007,040
Factor Arrows
2503,520
Factor Arrows
2251,760
Factor Arrows
2125,880
Factor Arrows
262,940
Factor Arrows
231,470
Factor Arrows
215,735
Factor Arrows
35,245
Factor Arrows
51,049

More Prime Factorization Examples

64,450,55864,450,55964,450,56164,450,562
21 x 32,225,2791371 x 1311 x 13,297171 x 1791 x 51,437121 x 111 x 2,929,5711

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