प्लान

अभाज्य गुणनखंडन कैलकुलेटर

इसके अभाज्य गुणनखंड देखने के लिए 2 से 1,000,000,000,000 तक कोई पूर्ण संख्या लिखें।

नतीजा

मान डालें और नतीजा देखने के लिए “गणना करें” दबाएँ।

सूत्र

n=p1e1×p2e2×⋯n = p_1^{e_1} \times p_2^{e_2} \times \cdots

Every whole number above 1 is a product of primes in exactly one way (the fundamental theorem of arithmetic).

d(n)=(e1+1)(e2+1)⋯d(n) = (e_1 + 1)(e_2 + 1)\cdots

The number of divisors comes straight from the exponents.

यह कैलकुलेटर कैसे इस्तेमाल करें

  1. Enter the number without separators, e.g. 360.
  2. Press Calculate. Each step divides out one prime.

हल किया गया उदाहरण

Prime factors of 360

360 ÷ 2³ = 45, 45 ÷ 3² = 5, and 5 is prime.

So 360 = 2³ × 3² × 5, with (3+1)(2+1)(1+1) = 24 divisors.

अक्सर पूछे जाने वाले सवाल

What are the prime factors of 54 and of 24?

54 = 2 × 3³ (divide by 2 to get 27, then by 3 three times), and 24 = 2³ × 3 (halve three times to get 3). For all the factors, not just the primes, use the factors calculator.

Is 1 a prime number?

No. A prime has exactly two divisors, 1 and itself; 1 has only one.

Why is there an upper limit?

Factorising very large numbers takes a long time. Up to one trillion, the result is guaranteed and instant.

और जानें