Q: What is the prime factorization of the number 61,402,541?

 A:
  • The prime factors are: 29 x 757 x 2,797
    • or also written as { 29, 757, 2,797 }
  • Written in exponential form: 291 x 7571 x 2,7971

Why is the prime factorization of 61,402,541 written as 291 x 7571 x 2,7971?

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 61,402,541

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 61,402,541 by 2

61,402,541 ÷ 2 = 30,701,270.5 - This has a remainder. Let's try another prime number.
61,402,541 ÷ 3 = 20,467,513.6667 - This has a remainder. Let's try another prime number.
61,402,541 ÷ 5 = 12,280,508.2 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
61,402,541 ÷ 29 = 2,117,329 - No remainder! 29 is one of the factors!
2,117,329 ÷ 29 = 73,011.3448 - There is a remainder. We can't divide by 29 evenly anymore. Let's try the next prime number
2,117,329 ÷ 31 = 68,300.9355 - This has a remainder. 31 is not a factor.
2,117,329 ÷ 37 = 57,225.1081 - This has a remainder. 37 is not a factor.
2,117,329 ÷ 41 = 51,642.1707 - This has a remainder. 41 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,117,329 ÷ 757 = 2,797 - No remainder! 757 is one of the factors!
2,797 ÷ 757 = 3.6948 - There is a remainder. We can't divide by 757 evenly anymore. Let's try the next prime number
2,797 ÷ 761 = 3.6754 - This has a remainder. 761 is not a factor.
2,797 ÷ 769 = 3.6372 - This has a remainder. 769 is not a factor.
2,797 ÷ 773 = 3.6184 - This has a remainder. 773 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
2,797 ÷ 2,797 = 1 - No remainder! 2,797 is one of the factors!

The orange divisor(s) above are the prime factors of the number 61,402,541. If we put all of it together we have the factors 29 x 757 x 2,797 = 61,402,541. It can also be written in exponential form as 291 x 7571 x 2,7971.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 61,402,541.

61,402,541
Factor Arrows
292,117,329
Factor Arrows
7572,797

More Prime Factorization Examples

61,402,53961,402,54061,402,54261,402,543
31 x 112 x 471 x 591 x 61122 x 51 x 3,070,127121 x 31 x 1,2911 x 7,9271411 x 1571 x 9,5391

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