Prime Factorization Calculator

Effortlessly find the prime factors of any positive integer with our Advanced Prime Factorization Calculator. This tool lists the prime factors and provides detailed results, including the exponent form, sum, product, distinct prime factors, and step-by-step factorization process. Perfect for students, teachers, and math enthusiasts looking to explore the intricacies of prime factorization.

Advanced Prime Factorization Calculator

Enter a positive integer:

Results:

Prime Factors:

Factorization (Exponent Form):

Number of Prime Factors:

Sum of Prime Factors:

Product of Prime Factors:

Distinct Prime Factors:

Largest Prime Factor:

Smallest Prime Factor:

Prime Factorization Steps:

Calculator

enter a positive integer in the input field

Results

Prime Factors: Lists all prime factors of the entered number.
Factorization (Exponent Form): Displays prime factors with their exponents.
Number of Prime Factors: Shows the count of prime factors.
The sum of Prime Factors: Total sum of all prime factors.
Product of Prime Factors: Product of all prime factors (should equal the original number).
Distinct Prime Factors: Lists unique prime factors.
Largest Prime Factor: Shows the largest prime factor.
Smallest Prime Factor: Shows the smallest prime factor.
Prime Factorization Steps: Displays step-by-step division process for factorization.

Examples

Prime Factorization of 234:

Divide by the smallest prime number (2):
234 is even, so we divide by 2.
234 ÷ 2 = 117
The first prime factor is 2.
Divide the result (117) by the next smallest prime number:
117 is not even, so we check the next smallest prime number, 3.
117 ÷ 3 = 39
The next prime factor is 3.
Continue dividing by the smallest prime number (3):
39 is also divisible by 3.
39 ÷ 3 = 13
So, another prime factor is 3.
Divide the result (13) by the next smallest prime number:
13 is a prime number itself, so it cannot be divided by any other prime number except 13.
13 ÷ 13 = 1
So, the last prime factor is 13.

Putting it all together, the prime factorization of 234 is:
234 = 2 * 3 * 3 * 13

Or, in exponent form: 234 = 2¹ * 3² * 13¹

Prime Factorization of 4627:

Check divisibility by the smallest prime number (2):
4627 is odd, so it is not divisible by 2.
Check divisibility by the next smallest prime number (3):
Sum of the digits of 4627: 4 + 6 + 2 + 7 = 19 
19 is not divisible by 3, so 4627 is not divisible by 3.
Check divisibility by the next smallest prime number (5):
4627 does not end in 0 or 5, so it is not divisible by 5.
Check divisibility by the next smallest prime number (7):
4627 ÷ 7 ≈ 661 (not an integer, so not divisible by 7)
Check divisibility by the next smallest prime number (11):
Alternating sum of the digits: 4 - 6 + 2 - 7 = -7 (not divisible by 11)
Check divisibility by the next smallest prime number (13):
4627 ÷ 13 ≈ 356    (not an integer, so not divisible by 13)
Check divisibility by the next smallest prime number (17):
4627 ÷ 17 ≈ 272 (not an integer, so not divisible by 17)
Check divisibility by the next smallest prime number (19):
4627 ÷ 19 ≈ 243  (not an integer, so not divisible by 19)
Check divisibility by the next smallest prime number (23):
4627 ÷ 23 ≈ 201 (not an integer, so not divisible by 23)
Check divisibility by the next smallest prime number (29):
4627 ÷ 29 ≈ 159.55 (not an integer, so not divisible by 29)
Check divisibility by the next smallest prime number (31):
4627 ÷ 31  ≈ 149.26 (not an integer, so not divisible by 31)
Check divisibility by the next smallest prime number (37):
4627 ÷ 37 = 125 (exact division, 4627 is divisible by 37)
So, 4627 ÷ 37 = 125
Factorize 125:
125 ÷ 5 = 25 
25 ÷ 5 = 5
5 ÷ 5 = 1

Putting it all together, the prime factorization of 4627 is:
 4627 = 37 * 5 * 5 * 5

In exponent form: 4627 = 37¹* 5³