Prime Factorization Calculator Formula

Understand the math behind the prime factorization calculator. Each variable explained with a worked example.

Use the Prime Factorization Calculator

Formulas Used

Div By 2

div_by_2 = mod(n, 2) == 0 ? 1 : 0

Div By 3

div_by_3 = mod(n, 3) == 0 ? 1 : 0

Div By 5

div_by_5 = mod(n, 5) == 0 ? 1 : 0

Div By 7

div_by_7 = mod(n, 7) == 0 ? 1 : 0

Sqrt N

sqrt_n = sqrt(n)

Is Even

is_even = mod(n, 2) == 0 ? 1 : 0

Variables

VariableDescriptionDefault
nNumber84

How It Works

Prime Factorization

What Is It?

Every integer greater than 1 can be written as a product of prime numbers in exactly one way (Fundamental Theorem of Arithmetic).

Method: Trial Division

1. Start with the smallest prime (2) 2. If it divides the number, it is a factor; divide and repeat 3. If not, try the next prime (3, 5, 7, 11, ...) 4. Stop when you reach sqrt(n)

Divisibility Quick Checks

  • By 2: last digit is even
  • By 3: digit sum is divisible by 3
  • By 5: last digit is 0 or 5

    • This calculator shows divisibility checks. For full factorization of large numbers, a step-by-step approach is needed.

    Worked Example

    Check divisibility of 84.

    n = 84
    1. 0184 / 2 = 42 (divisible by 2)
    2. 0284 / 3 = 28 (divisible by 3)
    3. 0384 / 5 = 16.8 (not divisible by 5)
    4. 0484 / 7 = 12 (divisible by 7)
    5. 0584 = 2² × 3 × 7

    Ready to run the numbers?

    Open Prime Factorization Calculator