Prime Factorization Calculator
Enter an integer to find its prime factorization (e.g. 360 = 2³ × 3² × 5), watch each division step, and see how many divisors the number has. Useful for simplifying fractions, GCD/LCM and number theory homework.
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TheCalculators — Prime Factorization Calculator
Printed thecalculators.com
360 =
2^3 × 3^2 × 5
6 prime factors (with multiplicity) · 24 divisors
- Prime factorization
- 2^3 × 3^2 × 5
- Is it prime?
- No — composite
- Prime factors (list)
- 2 × 2 × 2 × 3 × 3 × 5
- Distinct primes
- 2, 3, 5
- Total primes counted
- 6
- Number of divisors
- 24
- Smallest prime factor
- 2
- Largest prime factor
- 5
Division steps
- 1MethodRepeatedly divide by the smallest prime that fits, until the quotient is 1.
- 2Step 1: 360 ÷ 2= 180
- 3Step 2: 180 ÷ 2= 90
- 4Step 3: 90 ÷ 2= 45
- 5Step 4: 45 ÷ 3= 15
- 6Step 5: 15 ÷ 3= 5
- 7Step 6: 5 ÷ 5= 1
- 8Step End: Quotient reached 1 — factorization complete= 1
- 9Result360 = 2^3 × 3^2 × 5
Factorization working
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Formula
n = p₁^a₁ × p₂^a₂ × … (unique for every n > 1) · divisor count = (a₁+1)(a₂+1)…
Pro tips
- • Prime factorization is the backbone for GCD, LCM and simplifying fractions.
- • A number is a perfect square exactly when every exponent in its factorization is even.
- • Number of divisors = product of (exponent + 1) over all distinct primes.
FAQ
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