Q: What is the prime factorization of the number 77,044,480?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 23 x 2,617
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 5, 23, 2,617 }
  • Written in exponential form: 28 x 51 x 231 x 2,6171

Why is the prime factorization of 77,044,480 written as 28 x 51 x 231 x 2,6171?

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 77,044,480

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 77,044,480 by 2

77,044,480 ÷ 2 = 38,522,240 - No remainder! 2 is one of the factors!
38,522,240 ÷ 2 = 19,261,120 - No remainder! 2 is one of the factors!
19,261,120 ÷ 2 = 9,630,560 - No remainder! 2 is one of the factors!
9,630,560 ÷ 2 = 4,815,280 - No remainder! 2 is one of the factors!
4,815,280 ÷ 2 = 2,407,640 - No remainder! 2 is one of the factors!
2,407,640 ÷ 2 = 1,203,820 - No remainder! 2 is one of the factors!
1,203,820 ÷ 2 = 601,910 - No remainder! 2 is one of the factors!
601,910 ÷ 2 = 300,955 - No remainder! 2 is one of the factors!
300,955 ÷ 2 = 150,477.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
300,955 ÷ 3 = 100,318.3333 - This has a remainder. 3 is not a factor.
300,955 ÷ 5 = 60,191 - No remainder! 5 is one of the factors!
60,191 ÷ 5 = 12,038.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
60,191 ÷ 7 = 8,598.7143 - This has a remainder. 7 is not a factor.
60,191 ÷ 11 = 5,471.9091 - This has a remainder. 11 is not a factor.
60,191 ÷ 13 = 4,630.0769 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
60,191 ÷ 23 = 2,617 - No remainder! 23 is one of the factors!
2,617 ÷ 23 = 113.7826 - There is a remainder. We can't divide by 23 evenly anymore. Let's try the next prime number
2,617 ÷ 29 = 90.2414 - This has a remainder. 29 is not a factor.
2,617 ÷ 31 = 84.4194 - This has a remainder. 31 is not a factor.
2,617 ÷ 37 = 70.7297 - This has a remainder. 37 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,617 ÷ 2,617 = 1 - No remainder! 2,617 is one of the factors!

The orange divisor(s) above are the prime factors of the number 77,044,480. 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 5 x 23 x 2,617 = 77,044,480. It can also be written in exponential form as 28 x 51 x 231 x 2,6171.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 77,044,480.

77,044,480
Factor Arrows
238,522,240
Factor Arrows
219,261,120
Factor Arrows
29,630,560
Factor Arrows
24,815,280
Factor Arrows
22,407,640
Factor Arrows
21,203,820
Factor Arrows
2601,910
Factor Arrows
2300,955
Factor Arrows
560,191
Factor Arrows
232,617

More Prime Factorization Examples

77,044,47877,044,47977,044,48177,044,482
21 x 71 x 5,503,177131 x 2331 x 110,2211971 x 2271 x 3,499121 x 32 x 4,280,2491

Try the factor calculator

Explore more about the number 77,044,480:


Ask a Question