Q: What is the prime factorization of the number 760,631,261?

 A:
  • The prime factors are: 13 x 137 x 427,081
    • or also written as { 13, 137, 427,081 }
  • Written in exponential form: 131 x 1371 x 427,0811

Why is the prime factorization of 760,631,261 written as 131 x 1371 x 427,0811?

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 760,631,261

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 760,631,261 by 2

760,631,261 ÷ 2 = 380,315,630.5 - This has a remainder. Let's try another prime number.
760,631,261 ÷ 3 = 253,543,753.6667 - This has a remainder. Let's try another prime number.
760,631,261 ÷ 5 = 152,126,252.2 - This has a remainder. Let's try another prime number.
760,631,261 ÷ 13 = 58,510,097 - No remainder! 13 is one of the factors!
58,510,097 ÷ 13 = 4,500,776.6923 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
58,510,097 ÷ 17 = 3,441,770.4118 - This has a remainder. 17 is not a factor.
58,510,097 ÷ 19 = 3,079,478.7895 - This has a remainder. 19 is not a factor.
58,510,097 ÷ 23 = 2,543,917.2609 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
58,510,097 ÷ 137 = 427,081 - No remainder! 137 is one of the factors!
427,081 ÷ 137 = 3,117.3796 - There is a remainder. We can't divide by 137 evenly anymore. Let's try the next prime number
427,081 ÷ 139 = 3,072.5252 - This has a remainder. 139 is not a factor.
427,081 ÷ 149 = 2,866.3154 - This has a remainder. 149 is not a factor.
427,081 ÷ 151 = 2,828.351 - This has a remainder. 151 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
427,081 ÷ 427,081 = 1 - No remainder! 427,081 is one of the factors!

The orange divisor(s) above are the prime factors of the number 760,631,261. If we put all of it together we have the factors 13 x 137 x 427,081 = 760,631,261. It can also be written in exponential form as 131 x 1371 x 427,0811.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 760,631,261.

760,631,261
Factor Arrows
1358,510,097
Factor Arrows
137427,081

More Prime Factorization Examples

760,631,259760,631,260760,631,262760,631,263
31 x 253,543,753122 x 51 x 38,031,563121 x 31 x 411 x 3,091,997172 x 15,523,0871

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